https://wiki.swarma.org/api.php?action=feedcontributions&user=%E6%B0%B4%E6%89%8B9303&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-29T01:02:56Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E6%9C%8B%E5%8F%8B%E7%9A%84%E6%9C%8B%E5%8F%8B&diff=33254朋友的朋友2022-07-29T03:03:03Z<p>水手9303:/* 模因Meme(语言的演化) */</p>
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<div>此词条由彩云小译翻译,翻译字数共643,由水手9303整理校核,如发现错误,请见谅,并恳请告知。<br />
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{{Other uses|Friend of a Friend (disambiguation)}} <br />
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In [[sociology]], a '''friend of a friend''' is a human contact that exists because of a mutual friend. Person C is a friend of a friend of person A when there is a person B that is a [[friend]] of both A and C. Thus the human relation "friend of a friend" is a compound relation among friends, similar to the [[uncle]] and [[aunt]] relations of [[kinship]]. Though friendship is a [[symmetric relation|reciprocal relation]], the relation of a friend of a friend may not be a friendship, though it holds potential for coalition building and dissemination of information.<br />
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在'''[[社会学]](Sociology)'''中,'''朋友的朋友'''是因为共同的朋友而存在的人际关系。当甲和丙都是乙的朋友,丙就成为甲的朋友的朋友。因此,人际关系中的“朋友的朋友”是朋友之间的复合关系,类似于[[亲属关系]](kinship)中的舅舅与舅妈关系(舅妈如果没有成为你舅舅的妻子,就不会成为你的舅妈)。虽然友谊是一种[[对称关系|相互关系]](symmetric relation|reciprocal relation),但朋友的朋友的关系可能不是友谊,尽管它具有建立联盟和传播信息的潜力。<br />
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==平衡理论Balance theory==<br />
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{{Main|Balance theory}}<br />
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The tendency of a friend of a friend to become a friend was noted by [[Fritz Heider]],<ref name=":0"></ref> though he also considered the possibility that one of the friendships might breakdown, according to ''balance theory'', which his view of human triangles is called. According to Heider, the friend of a friend contact could be stressful enough to undermine one or another of the friendships. Extending the study of social dynamics caused by such friend-of-a-friend tensions to social networks beyond triangles, D. Cartwright and [[Frank Harary]] used [[signed graph]]s to indicate positive or negative sentiments between persons.<ref name=Frank1956>Cartwright, D. and [[Frank Harary]] (1956)[http://snap.stanford.edu/class/cs224w-readings/cartwright56balance.pdf Structural balance: a generalization of Heider's theory], [[Psychological Review]] 63: 277–293 link from [[Stanford University]]</ref> In 1963 [[Anatol Rapoport]] summarized the theory: "The hypothesis implies roughly that attitudes of the group members will change is such a way that one's friends' friends will tend to become one's friends, ..."<ref name=Antol1963>[[Anatol Rapoport]] (1963) "Mathematical models of social interaction", in [https://archive.org/details/handbookofmathem017893mbp ''Handbook of Mathematical Psychology'', v. 2], pp 493 to 580, especially 541, editors: R.A. Galanter, R.R. Lace, E. Bush, [[John Wiley & Sons]]</ref> In September 1975 [[Dartmouth College]] offered a symposium<ref name="Paul1979">Paul W. Holland & Samuel Leinhardt (editors) (1979) ''Perspectives on Social Network Research'', [[Academic Press]] {{ISBN|9780123525505}}</ref> on these dynamics.<br />
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[[弗里茨·海德]](Fritz Heider)<ref name=":0">[[Fritz Heider]] (1946) "Attitudes and Cognitive Organization", [[The Journal of Psychology]] 21: 107 to 21</ref> 注意到了朋友的朋友会成为朋友的倾向,根据他的平衡理论(他对人类的三角关系的观点被称为平衡理论),他也考虑了三者之间友谊有破裂的可能性。根据海德的说法,与朋友之友的社会关系,可能会有足够的压力,来破坏这两者或那两者之间的友谊关系。卡特赖特(D. Cartwright)和[[弗兰克·哈拉里]](Frank Harary)<ref name=Frank1956>Cartwright, D. and [[Frank Harary]] (1956)[http://snap.stanford.edu/class/cs224w-readings/cartwright56balance.pdf Structural balance: a generalization of Heider's theory], [[Psychological Review]] 63: 277–293 link from [[Stanford University]]</ref>将这种朋友之友的紧张关系(三角关系)引起社会动力学的研究,扩展到三角关系之外的社会关系网络,他们使用[[符号图]](signed graph)表示人与人之间的积极或消极情绪。1963年,[[阿纳托尔·拉波波特]](Anatol Rapoport)<ref name=Antol1963>[[Anatol Rapoport]] (1963) "Mathematical models of social interaction", in [https://archive.org/details/handbookofmathem017893mbp ''Handbook of Mathematical Psychology'', v. 2], pp 493 to 580, especially 541, editors: R.A. Galanter, R.R. Lace, E. Bush, [[John Wiley & Sons]]</ref> 总结了这一理论:“这个假设大致意味着群体成员的态度会发生改变,也就是,一个人的朋友之友会成为他的(直接的)朋友...”1975年9月,[[达特茅斯学院]](Dartmouth College)举办了一个关于这类动力学的研讨会<ref name="Paul1979">Paul W. Holland & Samuel Leinhardt (editors) (1979) ''Perspectives on Social Network Research'', [[Academic Press]] {{ISBN|9780123525505}}</ref> 。<br />
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Bo Anderson made an analysis of the friend-of-a-friend relationship in connection with his criticism of balance theory.<ref name=Bo1979>Bo Anderson (1979) "Cognitive Balance Theory and Social Network Analysis: Remarks on some fundamental theoretical matters", pages 453–69 in ''Perspectives on Social Network Research'', editors: Paul W. Holland & Samuel Leinhardt, [[Academic Press]], see page 458.</ref><br />
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博·安德森(Bo Anderson)结合对平衡理论的批判,对朋友之友的关系进行了分析<ref name=Bo1979>Bo Anderson (1979) "Cognitive Balance Theory and Social Network Analysis: Remarks on some fundamental theoretical matters", pages 453–69 in ''Perspectives on Social Network Research'', editors: Paul W. Holland & Samuel Leinhardt, [[Academic Press]], see page 458.</ref>。<br />
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We have all encountered cases in which somebody has said, "You should meet so-and-so", only to find that we have little in common with that person, even though he or she was introduced to us by a mutual friend...In ''some'' friendships the persons value the exclusiveness of their relationship and are therefore not likely to let others into it. Friends differ from acquaintances in that they are not merely slots in a grid of social network relationships, but are valued for their personal, ''unique'' qualities. Hence, when I relate to a friend of a friend, I need to know something about the perceptions and exchanges that make up this friendship. My reaction to my friend's friend (or spouse) may even be ''unfavorable'', although I may ''also'' well understand and sympathize with my friend’s affection for her, given ''his'' needs, perceptions, interests and so on. <br />
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我们都遇到过这样的情况,有人说: “你应该见见某某” ,结果却发现我们和那个人没有什么共同点,尽管他或她是由彼此共同的朋友介绍给我们的... ... 在“某些”友谊关系中,人们看重他们关系的排他性,因此不太可能让别人介入。朋友与熟人的不同之处在于,朋友不仅仅是社交网络关系网中的一个网格的占位,而且因其个人的独特品质而受到重视。因此,当我与朋友的朋友建立联系时,我需要了解构成这种友谊的看法,并相互交流。我对朋友的朋友(或配偶)的反应,甚至可能是“不利的”,尽管我考虑到朋友的需要、看法、兴趣等等之后,“也”能理解和同情我的朋友对她的感情。<br />
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Considering [[friendship]] between people to be a [[binary relation]], the connection to a friend of a friend is a [[composition of relations|composition]] of the relationship with itself. Composed relations are used to describe [[kinship#Composition of relations|kinship]], so it may be natural to apply composition to friendship. One consequence is that frequently a person's friends have more friends than him (the [[friendship paradox]]), which accents the reach of the compound connection. But the fact that friendship is not automatically a [[transitive relation]] produces some social dynamics.<br />
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考虑到人与人之间的[[友谊]](friendship)是一种[[两人关系]](binary relation),与朋友的朋友的联系,从关系本身而言,是一种[[复合关系]](composition of relations)。[[复合关系]]是用来描述[[亲属关系#复合关系]](kinship#Composition of relations)的,所以,把这种“复合”用到友谊上,是自然而然的。一个后果是,一个人的朋友,经常比这个人有更多的朋友([[友谊悖论]]),这突出了复合关系的影响范围。但事实上,友谊并不会自动成为一种[[传递关系]](transitive relation),这就产生了某些社会动力学。<br />
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==模因Meme(语言的演化)==<br />
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'''Friend of a friend''' ('''FOAF''') is a phrase used to refer to someone that one does not know well, literally, a friend of a friend.<br />
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'''朋友之友'''('''FOAF''')是一个短语,用来指一个人并不熟悉的(字面上),一个朋友的朋友。<br />
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In some [[social sciences]], the phrase is used as a half-joking shorthand for the fact that much of the information on which people act comes from distant sources (as in "It happened to a friend of a friend of mine") and cannot be confirmed.<ref Name=CJ2009>{{cite journal |vauthors=Goodreau SM, Kitts JA, Morris M |title=Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks |journal=Demography |volume=46 |issue=1 |pages=103–25 |year=2009 |pmid=19348111 |pmc=2831261 |doi=10.1353/dem.0.0045}}</ref> It is probably best known from [[urban legend]] studies, where it was popularized by [[Jan Harold Brunvand]].<br />
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在一些[[社会科学]](social science)中,这个短语,半开玩笑地用来表示,人们行为所依据的许多信息来自遥远的源头(例如”这件事发生在我一个朋友的朋友身上”) ,而且无法得到证实<ref Name=CJ2009>{{cite journal |vauthors=Goodreau SM, Kitts JA, Morris M |title=Birds of a feather, or friend of a friend? Using exponential random graph models to investigate adolescent social networks |journal=Demography |volume=46 |issue=1 |pages=103–25 |year=2009 |pmid=19348111 |pmc=2831261 |doi=10.1353/dem.0.0045}}</ref>。它可能是最广为流传的[[都市传说]](urban legend),那些研究,由[[詹·哈洛德·布朗凡德]](Jan Harold Brunvand)推广。<br />
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The acronym ''FOAF'' was coined by [[Rodney Dale]] and used in his 1978 book ''The Tumour in the Whale: A Collection of Modern Myths''.<ref name=cb1978>{{cite book|title=Encyclopedia of Urban Legends, Updated and Expanded Edition|first=Jan Harold|last=Brunvand|authorlink=Jan Harold Brunvand|page=241|publisher=[[ABC-CLIO]]|year=2012|url=https://books.google.com/books?id=9xOb-19lXx8C&pg=PA241}}</ref><br />
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首字母缩写''FOAF''由[[罗德尼·戴尔]](Rodney Dale)创造,并在他1978年的《鲸鱼中的肿瘤: 现代神话集》一书中使用<ref name=cb1978>{{cite book|title=Encyclopedia of Urban Legends, Updated and Expanded Edition|first=Jan Harold|last=Brunvand|authorlink=Jan Harold Brunvand|page=241|publisher=[[ABC-CLIO]]|year=2012|url=https://books.google.com/books?id=9xOb-19lXx8C&pg=PA241}}</ref>。<br />
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==其它语言Other languages==<br />
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* "Dúirt bean liom go ndúirt bean léi" [[q:Irish proverbs|(Irish proverb)]] – similar [[Irish language]] term literally meaning ''a woman told me that a woman told her that...''<br />
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* "L'homme qui a vu l'homme qui a vu l'ours" [[q:French proverbs|(French proverb)]] – similar [[French language]] proverb literally meaning ''The man who saw the man who saw the bear'', in which the bear is never seen, only heard of.<ref>{{cite web|url=http://www.rottentomatoes.com/m/lhomme_qui_a_vu_lhomme_qui_a_vu_lours_2013/|title=L'homme qui a vu l'homme qui a vu l'ours|publisher=|accessdate=14 February 2018}}</ref><ref>{{cite web|url=https://www.nytimes.com/reviews/movies|title=Movie Reviews|date=13 February 2018|publisher=|accessdate=14 February 2018|via=NYTimes.com}}</ref><br />
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* "Un amigo me dijo que un amigo le dijo..." [[q:Spanish proverbs|(Spanish proverb)]] – meaning literally ''A friend told me that a friend told him that...''<br />
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*"Jedna paní povídala..." [[q: Czech proverbs|(Czech proverb)]] – similar [[Czech language]] proverb literally meaning ''One lady said...''<br />
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* "Teman kepada teman saya..." [[Indonesian language|Bahasa Indonesia]]; literally meaning ''friend of my friend''.<br />
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* "Babaturana babaturan urang..." [[Sundanese language|Basa Sunda]]; literally meaning ''friend of my friend''. There is another version of this phrase in Sundanese language, "''Babaturan dulur urang''", which means "friend of my relatives".<br />
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* "카더라..." [[Korean language|Korean]]; [[Gyeongsang dialect]] word literally meaning ''Who said that...''<br />
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* "Diz-se que..." or "Dizem que..." [[Portuguese language|Portuguese]]; literally meaning ''It is said that...'' or ''They say that...''<br />
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* "Freundesfreund" [[German language|German]]; literally meaning ''a friend's friend''<br />
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* "Umgani womgani wami" [[IsiZulu language]]; meaning ''my friend's friend''<br />
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*"朋友的朋友" or "我的friend的friend" [[Cantonese]] / [[Hong Kong English]]; meaning ''my friend's friend''<br />
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==网络本体语言Web ontology language==<br />
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{{main|FOAF (ontology)}}<br />
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In [[information science]], an [[ontology (information science)|ontology]] describes categories, properties and relations between concepts, data and entities. The phrase "Friend Of A Friend", converted to the acronym '''FAOF''', has been adopted in [[Web Ontology Language]]. It has been used in [[WebID]] for identifying correspondents, and to designate a secure authentication protocol.<ref Name=w3>[https://www.w3.org/wiki/Foaf%2Bssl Foaf+ssl] at [[W3.org]]</ref><br />
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在[[信息科学]](information science)中,[[本体]](ontology)描述了概念、数据和实体之间的类别、性质和关系。短语“朋友之友” ,转换为首字母缩略词''FAOF'',在[[网络本体语言]](Web Ontology Language)中,已经被采用。它已在[[网络身份证明]](WebID)中用于识别通信者,并指定安全的身份验证协议<ref Name=w3>[https://www.w3.org/wiki/Foaf%2Bssl Foaf+ssl] at [[W3.org]]</ref>。<br />
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== 参见See also ==<br />
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{{Wiktionary|FOAF}}<br />
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* [[个体之间的联系]](Interpersonal ties)<br />
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* [[六度分割]](Six degrees of separation)<br />
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==参考文献References==<br />
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{{reflist|40em}}<br />
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{{Social networking}}<br />
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[[Category:Urban legends]]<br />
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Category:Urban legends<br />
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类别: 都市传奇<br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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[[Category:Friendship]]<br />
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Category:Friendship<br />
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分类: 友谊<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Friend of a friend]]. Its edit history can be viewed at [[朋友的朋友/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33253社交网络上的谣言传播2022-07-29T02:59:17Z<p>水手9303:/* 社会网络中的传染病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
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[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
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===传染病模型Epidemic models===<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. <br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点 i 的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点 i 和节点 j 相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
<br />
Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state.<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点 i 和节点 j 相互作用,其中一个将改变其状态。<br />
<br />
<br />
<br />
The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br/><br />
<br />
<br />
转移矩阵依赖于节点 i 和节点 j 的联系数,以及节点 i 和节点 j 的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点 i 处于状态I,节点 j 处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点 j 处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点 i 处于状态I,节点 j 处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
===参考文献References===<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33252社交网络上的谣言传播2022-07-29T02:54:20Z<p>水手9303:/* 社会网络中的传染病模型Epidemic models in social network */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br/> <br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
===参考文献References===<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33251社交网络上的谣言传播2022-07-29T02:49:49Z<p>水手9303:/* 小世界中的传染病模型Epidemic Models in Small-World Network */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
===参考文献References===<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33250社交网络上的谣言传播2022-07-29T02:48:35Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
===参考文献References===<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33249社交网络上的谣言传播2022-07-29T02:44:54Z<p>水手9303:/* 参考文献References */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
===参考文献References===<br />
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<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33248社交网络上的谣言传播2022-07-29T02:44:34Z<p>水手9303:</p>
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
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===传染病模型Epidemic models===<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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===社会网络中的传染病模型Epidemic models in social network===<br />
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We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
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=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
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微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
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===信息级联模型information cascade===<br />
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===线性阈值模型Linear threshold models===<br />
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===能量模型Energy model=== <br />
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===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
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HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
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The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
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HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
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First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
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首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33246社交网络上的谣言传播2022-07-29T02:43:51Z<p>水手9303:</p>
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[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
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===传染病模型Epidemic models===<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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===社会网络中的传染病模型Epidemic models in social network===<br />
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We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
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=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
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微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
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===信息级联模型information cascade===<br />
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===线性阈值模型Linear threshold models===<br />
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===能量模型Energy model=== <br />
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===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
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HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
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The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
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HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33245社交网络上的谣言传播2022-07-29T02:43:26Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
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HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络(OSN)]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络(OSN)]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33244社交网络上的谣言传播2022-07-29T02:42:07Z<p>水手9303:/* 微观模型Microscopic models */</p>
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<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
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[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
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<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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===社会网络中的传染病模型Epidemic models in social network===<br />
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We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref name=HISB>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> ,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33243社交网络上的谣言传播2022-07-29T02:40:41Z<p>水手9303:/* 微观模型Microscopic models */</p>
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<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
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[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型(information cascade)]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33242社交网络上的谣言传播2022-07-29T02:40:03Z<p>水手9303:/* 小世界中的传染病模型Epidemic Models in Small-World Network */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群(local clustering)]] ,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界(small world)]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33241社交网络上的谣言传播2022-07-29T02:38:23Z<p>水手9303:/* 社会网络中的传染病模型Epidemic models in social network */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵(adjacency matrix)]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)]](图论); <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33240社交网络上的谣言传播2022-07-29T02:30:44Z<p>水手9303:</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往(social communication)]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33239社交网络上的谣言传播2022-07-29T02:29:35Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
===HISB模型 HISB model===<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33238社交网络上的谣言传播2022-07-29T02:29:04Z<p>水手9303:/* 传染病模型Epidemic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
===传染病模型Epidemic models===<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33237社交网络上的谣言传播2022-07-29T02:28:48Z<p>水手9303:/* 谣言传播模型Rumor Propagation Models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
===谣言传播模型Rumor Propagation Models ===<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33235社交网络上的谣言传播2022-07-29T02:27:36Z<p>水手9303:/* 小世界中的传染病模型Epidemic Models in Small-World Network */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===小世界中的传染病模型Epidemic Models in Small-World Network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world Network|Small World]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33234社交网络上的谣言传播2022-07-29T02:23:12Z<p>水手9303:/* 传染病模型Epidemic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[Compartmental models in epidemiology|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33233社交网络上的谣言传播2022-07-29T02:21:17Z<p>水手9303:/* 传染病模型Epidemic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和谣言抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 谣言抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33232社交网络上的谣言传播2022-07-29T02:19:33Z<p>水手9303:/* 传染病模型Epidemic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as I, S, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为I、S和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33231社交网络上的谣言传播2022-07-29T02:17:20Z<p>水手9303:/* 传染病模型Epidemic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
====传染病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33230社交网络上的谣言传播2022-07-29T02:16:58Z<p>水手9303:/* 宏观模型Macroscopic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33229社交网络上的谣言传播2022-07-29T02:15:43Z<p>水手9303:/* 宏观模型Macroscopic models */</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于传染病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33228社交网络上的谣言传播2022-07-29T02:14:08Z<p>水手9303:</p>
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观视角主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
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==== 流行病模型Epidemic models====<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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===社会网络中的传染病模型Epidemic models in social network === <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
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=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
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微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
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===信息级联模型information cascade===<br />
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===线性阈值模型Linear threshold models===<br />
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===能量模型Energy model=== <br />
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====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
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HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
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The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
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HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
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First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
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首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33227社交网络上的谣言传播2022-07-29T02:12:44Z<p>水手9303:</p>
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[[Rumor]] is an important form of [[social communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是[[社会交往social communication]]的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
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==== 流行病模型Epidemic models====<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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===社会网络中的传染病模型Epidemic models in social network === <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
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=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
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微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
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===信息级联模型information cascade===<br />
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===线性阈值模型Linear threshold models===<br />
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===能量模型Energy model=== <br />
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====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
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HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
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The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
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HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33225社交网络上的谣言传播2022-07-29T02:11:39Z<p>水手9303:</p>
<hr />
<div>此词条由彩云小译初步翻译,由水手9303整理,若有错误或不当之处,请见谅,并恳请告知。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33224社交网络上的谣言传播2022-07-29T02:09:00Z<p>水手9303:/* 社会网络中的传染病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33223社交网络上的谣言传播2022-07-29T02:08:39Z<p>水手9303:/* 社会网络中的传染病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的流行病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
===社会网络中的传染病模型Epidemic models in social network === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33222社交网络上的谣言传播2022-07-29T02:08:12Z<p>水手9303:/* 社会网络中的流行病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
===社会网络中的流行病模型Epidemic models in social network===<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
=== 社会网络中的传染病模型 === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33221社交网络上的谣言传播2022-07-29T02:07:17Z<p>水手9303:/* 社会网络中的传染病模型 */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
=== 社会网络中的传染病模型 === <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33220社交网络上的谣言传播2022-07-29T02:05:34Z<p>水手9303:/* HISB模型 HISB model */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in [[OSN]]s, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through [[OSN]]s.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33218社交网络上的谣言传播2022-07-29T02:03:24Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: "When does an individual spread a rumor? When does an individual accept rumors? In which [[OSN]] does this individual spread the rumors?''.<br />
<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突显其对谣言传播的影响。该模型试图回答以下问题:“一个人什么时候散布谣言?一个人什么时候会接受谣言?这个人在哪个社交网站上散布谣言。”<br />
<br />
<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISB model propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
<br />
首先,它提出了一种类似于阻尼谐波运动的谣言个体行为公式,该公式在传播过程中纳入了个体的意见。此外,它还建立了个体间谣言传播的规则。就这样,它呈现了HISB模型传播过程,其中引入了新的指标,以准确评估谣言通过[[在线社交网络OSN]]传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33215社交网络上的谣言传播2022-07-29T01:40:58Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which [[OSN]] does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
<br />
HISB模型提出了一种与文献中其他模型平行的方法,更关注个人如何传播谣言。,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 在线社交网络传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33214社交网络上的谣言传播2022-07-29T01:39:35Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
<br />
<br />
<br />
HISB模型是一个谣言传播模型,它可以再现这种现象的趋势,并提供指标评估谣言的影响,从而有效地了解其扩散过程并减少其影响。人性中存在的多样性,使得人们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体行为和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。<br />
<br />
The HISB model proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which [[OSN]] does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
<br />
因此,它试图了解个人的行为,以及他们在[[在线社交网络OSN]]的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 在线社交网络传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33211社交网络上的谣言传播2022-07-29T01:17:05Z<p>水手9303:/* HISB模型 HISB model */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
====HISB模型 HISB model====<br />
The HISB model is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33209社交网络上的谣言传播2022-07-29T01:16:09Z<p>水手9303:/* 能量模型Energy model */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
===能量模型Energy model=== <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33208社交网络上的谣言传播2022-07-29T01:15:40Z<p>水手9303:/* 线性阈值模型Linear threshold models */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models===<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33207社交网络上的谣言传播2022-07-29T01:15:12Z<p>水手9303:/* 线性阈值模型Linear threshold models */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
===线性阈值模型Linear threshold models=== <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33206社交网络上的谣言传播2022-07-29T01:14:28Z<p>水手9303:/* 信息级联模型information cascade */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
<br />
<br />
微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
===信息级联模型information cascade===<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
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[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
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==== 流行病模型Epidemic models====<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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= = = 社会网络中的传染病模型 = = = <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
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=== 微观模型Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>, the energy model<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB model <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>.<br />
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微观方法在个体的相互作用中吸引了更多的注意力: “谁影响了谁”。这一类中,知名的模型有:[[independent cascades|信息级联模型information cascade]]和线性阈值模型<ref name=kempw>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref>,能量模型<ref name=han2014>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref>, HISB模型<ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref>,以及格莱姆(Galam)模型<ref name=galam>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref>。<br />
<br />
= = = 独立级联模型 = = = <br />
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==== Linear threshold models ====<br />
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==== Linear threshold models ====<br />
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= = = = 线性阈值模型 = = = <br />
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==== Energy model ====<br />
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==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
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==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33203社交网络上的谣言传播2022-07-29T00:53:46Z<p>水手9303:/* = = 社会网络中的传染病模型 = = */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[Small-world network|小世界small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33202社交网络上的谣言传播2022-07-29T00:53:00Z<p>水手9303:/* = = 社会网络中的传染病模型 = = */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个[[小世界Small-world network|small world]]的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33201社交网络上的谣言传播2022-07-29T00:50:44Z<p>水手9303:/* = = 社会网络中的传染病模型 = = */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个小世界的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期,谣言会传播得很广。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,他由下面的公式给出:<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
完全混合的人群网络中,一个没有阈值的传播过程,在小世界中表现出明显的相变。下图说明了<math>r_\infty</math>的渐近值作为重布线概率<math>p</math>的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33200社交网络上的谣言传播2022-07-29T00:27:25Z<p>水手9303:/* = = 社会网络中的传染病模型 = = */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的[[群聚系数|本地集群]],那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一(辟谣),他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,这是由<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33198社交网络上的谣言传播2022-07-28T14:45:37Z<p>水手9303:/* = = 社会网络中的传染病模型 = = */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的本地集群,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一,他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
<br />
<br />
我们还可以计算最终传播消息的人数,这是由<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33197社交网络上的谣言传播2022-07-28T14:39:21Z<p>水手9303:/* 社会网络中的流行病模型Epidemic models in social network */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
1= We initial rumor to a single node <math>i</math>;<br />
<br />
2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
3= Then have the choice: <br />
<br />
ordered list<br />
<br />
3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
<br />
3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度Degree(图论)]]; <br />
<br />
<br />
3= 然后选择: <br />
<br />
操作表<br />
<br />
3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
<br />
3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
<br />
4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is small world, that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的本地集群,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一,他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br />
r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} <br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of r_\infty as a function of the rewiring probability p.<br />
<br />
我们还可以计算最终传播消息的人数,这是由 r _ infty = 1-e ^ {-({ alpha + beta over beta }) r _ infty 给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
<br />
[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33196社交网络上的谣言传播2022-07-28T14:38:19Z<p>水手9303:/* 社会网络中的流行病模型Epidemic models in social network */</p>
<hr />
<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
<br />
{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
<br />
[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
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== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
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在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
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===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
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第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
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==== 流行病模型Epidemic models====<br />
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A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
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一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
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*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
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*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
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The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
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通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
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One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
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一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
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{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
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::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
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::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
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{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
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::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
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Of course we always have conservation of individuals:<br />
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<math> N=I+S+R </math><br />
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当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
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The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
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Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
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:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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可以写成:<br />
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:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
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Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
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与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
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==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
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The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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ordered list<br />
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1= We initial rumor to a single node <math>i</math>;<br />
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2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
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3= Then have the choice: <br />
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ordered list<br />
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3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
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3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
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4= We pick another node who is a spreader at random, and repeat the process.<br />
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我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
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这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
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转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
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网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
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操作表<br />
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1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
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2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
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<math>p_j={A_{ji} \over k_i}</math> <br /><br />
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其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)(图论)]]; <br />
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3= 然后选择: <br />
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操作表<br />
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3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
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3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
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4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
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= = = 社会网络中的传染病模型 = = = <br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is small world, that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
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我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的本地集群,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一,他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
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Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
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Also we can compute the final number of people who once spread the news, this is given by<br />
r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} <br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of r_\infty as a function of the rewiring probability p.<br />
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我们还可以计算最终传播消息的人数,这是由 r _ infty = 1-e ^ {-({ alpha + beta over beta }) r _ infty 给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
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=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
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==== Independent cascades models ====<br />
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==== Independent cascades models ====<br />
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= = = 独立级联模型 = = = <br />
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==== Linear threshold models ====<br />
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==== Linear threshold models ====<br />
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= = = = 线性阈值模型 = = = <br />
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==== Energy model ====<br />
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==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
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==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
<br />
<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33195社交网络上的谣言传播2022-07-28T14:35:50Z<p>水手9303:/* 社会网络中的流行病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
|1= We initial rumor to a single node <math>i</math>;<br />
<br />
|2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
|3= Then have the choice: <br />
<br />
ordered list<br />
|3.1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
|3.2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
|4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
|1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
|2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)(图论)]]; <br />
<br />
|3= 然后选择: <br />
<br />
操作表<br />
|3.1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
|3.2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
|4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is small world, that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的本地集群,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一,他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br />
r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} <br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of r_\infty as a function of the rewiring probability p.<br />
<br />
我们还可以计算最终传播消息的人数,这是由 r _ infty = 1-e ^ {-({ alpha + beta over beta }) r _ infty 给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
<br />
==== Independent cascades models ====<br />
<br />
==== Independent cascades models ====<br />
<br />
= = = 独立级联模型 = = = <br />
<br />
==== Linear threshold models ====<br />
<br />
==== Linear threshold models ====<br />
<br />
= = = = 线性阈值模型 = = = <br />
<br />
==== Energy model ====<br />
<br />
==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
<br />
==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
<br />
== References ==<br />
<br />
== References ==<br />
<br />
= = 参考文献 = =<br />
<br />
<references /><br />
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[[Category:Social networks]]<br />
<br />
Category:Social networks<br />
<br />
分类: 社交网络<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>水手9303https://wiki.swarma.org/index.php?title=%E7%A4%BE%E4%BA%A4%E7%BD%91%E7%BB%9C%E4%B8%8A%E7%9A%84%E8%B0%A3%E8%A8%80%E4%BC%A0%E6%92%AD&diff=33194社交网络上的谣言传播2022-07-28T14:22:55Z<p>水手9303:/* 社会网络中的流行病模型Epidemic models in social network */</p>
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<div>此词条由彩云小译初步翻译,翻译字数共1449,未经人工整理和审校,带来阅读不便,请见谅。<br />
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{{multiple issues|<br />
{{notability|date=June 2012}}<br />
{{Original research|date=June 2012}}<br />
}}<br />
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[[Rumor]] is an important form of social [[communication]]s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.<br />
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a [[stochastic process]] in social networks.<br />
While the microscopic models are more interested more on the micro interactions between individuals.<br />
<br />
<br />
<br />
[[谣言(Rumor)]]是社会交往的一种重要形式,谣言的传播在人类生活的各种事物中都发挥着重要作用。研究谣言传播过程有两种方法: 微观模型和宏观模型。宏观模型提出的宏观观点主要是基于广泛使用的戴利-肯德尔(Daley-Kendall)模型和马奇-汤普森(Maki-Thompson)模型。特别是,我们可以把谣言看作是社交网络中的[[随机过程(stochastic process)]]。而微观模型对个体间的微观相互作用更感兴趣。<br />
<br />
== 谣言传播模型Rumor propagation Models ==<br />
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.<br />
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.<br />
<br />
<br />
在过去的几年里,人们对在线社交网络中的谣言传播问题越来越感兴趣,人们提出了不同的方法来研究它。通过仔细研究现有文献,我们将这些著作分为宏观和微观两类方法。<br />
<br />
===宏观模型Macroscopic models ===<br />
The first category is mainly based on the Epidemic models <ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref> where the pioneering research engaging rumor propagation under these models started during the 1960s.<br />
<br />
<br />
<br />
<br />
第一类主要基于流行病模型年随机传播<ref name=DK1965>Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.</ref>。通过这些模型下,从事谣言传播的开创性研究始于1960年代。<br />
<br />
==== 流行病模型Epidemic models====<br />
<br />
A standard model of rumor spreading was introduced by Daley and Kendall,<ref name=DK1965></ref>. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:<br />
<br />
<br />
<br />
一个谣言传播的标准模型是由戴利(Daley)和肯德尔(Kendall)<ref name=DK1965></ref>。假设总共有N个人,传播网络中的这些人可以分为三类:无知者(ignorants)、传播者(spreaders)和抑制者(stiflers),分别在下文中表示为S、I和R:<br />
<br />
*I: people who are ignorant of the rumor;<br />
*S: people who actively spread the rumor;<br />
*R: people who have heard the rumor, but no longer are interested in spreading it.<br />
<br />
<br />
*I: 无知者(ignorants),对谣言一无所知的人; <br />
*S: 传播者(spreaders),积极散布谣言的人; <br />
*R: 抑制者(stiflers),听说过谣言但不再有兴趣散布谣言的人。<br />
<br />
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.<br />
<br />
<br />
<br />
通过传播者与跟他一对一接触的人,谣言在人群中传播。任何两人一对一时,传播者都试图用谣言“感染”另一个人。一种情况,另一个人是无知者时,(已经知道谣言的)他或她,就会成为一个传播者。另外两种情况,两个人都知道谣言,两个人或其中一个人,知道这个谣言是假的,并决定不再传播谣言,他们就会成为谣言抑制者。<br />
<br />
One variant is the Maki-Thompson model<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref> .In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
::which says when a spreader meet an ignorant, the ignorant will become a spreader. <br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
::which says when two spreaders meet with each other, one of them will become a stifler.<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.<br />
<br />
<br />
一种变体是梅基-汤普森(Maki-Thompson)模型<ref name=maki>Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.</ref>。在这个模型中,谣言是通过传播者与人群中其他人的直接接触来传播的。此外,当一个传播者遇到另一个传播者时,只有先前的传播者会成为谣言抑制者。这样,三种类型的相互作用可以以一定的速率发生。<br />
<br />
{{NumBlk|;<math>\begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix}</math>|{{EquationRef|1}}}}<br />
<br />
::就是说,当传播者遇到无知者时,无知者会成为一个传播者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix}</math>|{{EquationRef|2}}}}<br />
<br />
::就是说,当两个传播者相遇时,其中一个传播者会变成谣言抑制者。<br />
<br />
{{NumBlk|;|<math>\begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix}</math>|{{EquationRef|3}}}}<br />
<br />
::就是说,当一个传播者遇到一个谣言抑制者时,他会失去传播谣言的兴趣,也成为一个谣言抑制者。<br />
<br />
Of course we always have conservation of individuals:<br />
<br />
<math> N=I+S+R </math><br />
<br />
<br />
当然,总人数是守恒的: <br />
<math> N=I+S+R </math><br />
<br />
The change in each class in a small time interval is:<br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
每类在很小时间间隔内的变化是: <br/><br />
:<math> \Delta S \approx - \Delta t \alpha IS/N</math><br />
:<math> \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]</math><br />
:<math> \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] </math><br />
<br />
<br />
Since we know <math>S</math>, <math>I</math> and <math>R</math> sum up to <math>N</math>, we can reduce one equation from the above, which leads to a set of differential equations using relative variable <math>x=I/N</math> and <math>y=S/N</math> as follows<br /><br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
which we can write<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
由于我们知道<math>S</math>, <math>I</math> 的和 <math>R</math> 等于<math>N</math>,我们可以从上面去掉一个方程,用相对变量<math>x=I/N</math> 和 <math>y=S/N</math> 导出一组微分方程如下:<br />
<br />
:<math> {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
可以写成:<br />
<br />
:<math> {dx \over dt} = (\alpha + \beta)xy - \beta x </math><br />
:<math> {dy \over dt} = - \alpha xy</math><br />
<br />
<br />
<br />
Compared with the ordinary [[Compartmental models in epidemiology|SIR model]], we see that the only difference to the ordinary [[Compartmental models in epidemiology|SIR model]] is that we have a factor <math>\alpha + \beta</math> in the first equation instead of just <math>\alpha</math>. We immediately see that the ignorants can only decrease since <math>x,y\ge 0</math> and <math>{dy \over dt}\le 0</math>. Also, if<br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
which means<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.<br />
<br />
<br />
与一般的[[流行病学中的隔室模型|SIR模型]]相比,我们发现与一般SIR模型的唯一区别在于,我们在第一个方程中有一个因子<math>\alpha + \beta</math>,而不仅仅是<math>\alpha </math>。我们立即看到,当<math>x,y\ge 0</math> 和 <math>{dy \over dt}\le 0</math>时,无知者开始减少。此外,如果: <br /><br />
:<math>R_0={\alpha +\beta \over \beta} >1 </math><br />
这意味着<br /><br />
:<math>{\alpha \over \beta}>0</math><br />
即使在任意小的速率参数下,谣言模型也表现出“流行性”。<br />
<br />
==== 社会网络中的流行病模型Epidemic models in social network ====<br />
We model the process introduced above on a network in discrete time, that is, we can model it as a DTMC. Say we have a network with N nodes, then we can define <math> X_i(t)</math> to be the state of node i at time t. Then <math>X(t)</math> is a stochastic process on <math>S=\{S,I,R\}^N</math>. At a single moment, some node i and node j interact with each other, and then one of them will change its state. Thus we define the function <math>f</math> so that for <math>x</math> in <math>S</math>,<math>f(x,i,j)</math> is when the state of network is <math>x</math>, node i and node j interact with each other, and one of them will change its state. The transition matrix depends on the number of ties of node i and node j, as well as the state of node i and node j. For any <math>y=f(x,i,j)</math>, we try to find <math>P(x,y)</math>. If node i is in state I and node j is in state S, then <math>P(x,y)=\alpha A_{ji}/k_i</math>; if node i is in state I and node j is in state I, then <math>P(x,y)=\beta A_{ji}/k_i</math>; if node i is in state I and node j is in state R, then <math>P(x,y)=\beta A_{ji}/k_i</math>. <br />
For all other <math>y</math>, <math>P(x,y)=0</math>.<br />
<br />
<br/> <br />
The procedure on a network is as follows<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
ordered list<br />
<br />
|1= We initial rumor to a single node <math>i</math>;<br />
<br />
|2= We pick one of its neighbors as given by the [[adjacency matrix]], so the probability we will pick node <math>j</math> is <br /><br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
where <math>A_{ji}</math> is from the adjacency matrix and <math>A_{ji}=1</math> if there is a tie from <math>i</math> to <math>j</math>, and <math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> is the [[Degree (graph theory)|degree]] for node <math>i</math>; <br />
<br />
|3= Then have the choice: <br />
<br />
ordered list<br />
|1= If node <math>j</math> is an ignorant, it becomes a spreader at a rate <math>\alpha</math>;<br />
|2= If node <math>j</math> is a spreader or stifler, then node <math>i</math> becomes a stifler at a rate <math>\beta</math>. <br />
<br />
|4= We pick another node who is a spreader at random, and repeat the process.<br />
<br />
<br />
<br />
我们对上面介绍的过程,在离散时间的网络上建模,也就是说,我们可以将它建模为一个离散时间马尔可夫链(DTMC)。假设我们有一个N个节点的网络,那么我们可以定义<math> X_i(t)</math>为t时刻的节点i的状态。那么<math>X(t)</math>是<math>S=\{S,I,R\}^N</math>上的随机过程。在某一时刻,某个节点i和节点j相互作用,然后其中一个节点将改变其状态。<br />
<br />
<br />
这样,我们定义一个函数<math>f</math> ,使得对于<math>S</math>中的<math>x</math> ,<math>f(x,i,j)</math> 是,当网络状态为<math>x</math>时,节点i和节点j相互作用,其中一个将改变其状态。<br />
<br />
<br />
转移矩阵依赖于节点i和节点j的联系数,以及节点i和节点j的状态。对于任意<math>y=f(x,i,j)</math>,我们设法求<math>P(x,y)</math>。如果节点i处于状态I,节点j处于状态S,则<math>P(x,y)=\alpha A_{ji}/k_i</math>; 如果节点 i 处于状态I,节点j处于状态S,则 p (x,y) = beta a _ { ji }/k _ i; 如果节点i处于状态I,节点j处于状态R,则<math>P(x,y)=\beta A_{ji}/k_i</math>。对于所有其他<math>y</math>,<math>P(x,y)=0</math>。<br />
<br />
<br />
网络环境下的操作步骤如下<ref name=Brockmann> Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University</ref> :<br />
<br />
<br />
操作表<br />
<br />
|1= 我们把谣言初始化赋予给节点 <math>i</math>;<br />
<br />
<br />
|2= 从[[临接矩阵adjacency matrix]]中,我们选择一个它的临近节点<math>j</math>, 它成为谣言传播者的概率是 <br /><br />
<br />
<math>p_j={A_{ji} \over k_i}</math> <br /><br />
<br />
其中<math>A_{ji}</math> 来自于临接矩阵,且如果有从节点<math>i</math>到节点<math>j</math>的连接,那么<math>A_{ji}=1</math> ,且<math>k_i= \textstyle \sum_{j=1}^N A_{ij}</math> 是节点<math>i</math>的[[度(Degree)(图论)]]; <br />
<br />
|3= 然后选择: <br />
操作表<br />
|1= 如果节点 <math>j</math> 是无知者,它成为一个传播者的速率是 <math>\alpha</math>;<br />
|2= 如果节点 <math>j</math> 是一个传播者或谣言抑制者, 那么节点<math>i</math> 成为一个谣言抑制者的速率是 <math>\beta</math>。<br />
<br />
|4= 我们随机选择一个是传播者的节点, 并重复这一过程。<br />
<br />
= = = 社会网络中的传染病模型 = = = <br />
<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong [[Clustering coefficient|local clustering]] around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is [[Small-world network|small world]], that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
We would expect that this process spreads the rumor throughout a considerable fraction of the network. Note however that if we have a strong local clustering around a node, what can happen is that many nodes become spreaders and have neighbors who are spreaders. Then, every time we pick one of those, they will recover and can extinguish the rumor spread. On the other hand, if we have a network that is small world, that is, a network in which the shortest path between two randomly chosen nodes is much smaller than that one would expect, we can expect the rumor spread far away.<br />
<br />
我们可以预期这个过程会在网络的相当一部分中传播谣言。但是请注意,如果我们在一个节点周围有一个强大的本地集群,那么可能发生的情况是,许多节点成为传播者,并且有作为传播者的邻居。然后,每次我们选择其中之一,他们将恢复,并可以消除谣言传播。另一方面,如果我们有一个世界很小的网络,也就是说,在一个网络中,两个随机选择的节点之间的最短路径比预期的要小得多,我们可以预期谣言会传播得很远。<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br /><br />
<math>r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty}</math> <br /><br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of <math>r_\infty</math> as a function of the rewiring probability <math>p</math>.<br />
<br />
Also we can compute the final number of people who once spread the news, this is given by<br />
r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} <br />
In networks the process that does not have a threshold in a well mixed population, exhibits a clear cut phase-transition in small worlds. The following graph illustrates the asymptotic value of r_\infty as a function of the rewiring probability p.<br />
<br />
我们还可以计算最终传播消息的人数,这是由 r _ infty = 1-e ^ {-({ alpha + beta over beta }) r _ infty 给出的。在网络中,在一个完全混合的人口中没有一个阈值的过程,在小世界中表现出明显的相变。下图说明了 r _ infty 的渐近值作为重新布线概率 p 的函数。<br />
<br />
=== Microscopic models ===<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the [[independent cascades|information cascade]] and the linear threshold models,<ref>[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769.</ref> the energy model,<ref>S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003.</ref> HISBmodel <ref>A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018..</ref> and Galam's Model.<ref>S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.</ref><br />
<br />
The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom."<br />
The known models in this category are the information cascade and the linear threshold models,[1] D. Kempe, J. Kleinberg, É. Tardos, Maximizing the spread of influence through a social network, Proc. Ninth ACM SIGKDD Int. Conf. Knowl. Discov. Data Min. - KDD ’03. (2003) 137. doi:10.1145/956755.956769. the energy model,S. Han, F. Zhuang, Q. He, Z. Shi, X. Ao, Energy model for rumor propagation on social networks, Phys. A Stat. Mech. Its Appl. 394 (2014) 99–109. doi:10.1016/j.physa.2013.10.003. HISBmodel A.I.E. Hosni, K. Li, S. Ahmed, HISBmodel : A Rumor Diffusion Model Based on Human Individual and Social Behaviors in Online Social Networks, in: Springer, 2018.. and Galam's Model.S. Galam, Modelling rumors: The no plane Pentagon French hoax case, Phys. A Stat. Mech. Its Appl. 320 (2003) 571–580. doi:10.1016/S0378-4371(02)01582-0.<br />
<br />
= = = 微观模型 = = = 微观方法在个体的相互作用中吸引了更多的注意: “谁影响了谁”这一类中已知的模型是信息级联模型和线性阈值模型。通过社交网络最大化影响力的传播。第九届 ACM SIGKDD Int。机密文件。Knowl.迪斯科舞厅。资料分析。ー KDD’03。(2003)137. doi: 10.1145/956755.956769.能量模型 s。韩,庄峰峰,q。何志志,石,社交网络谣言传播的能量模型,体育。统计数据。机械。它的应用。394 (2014) 99–109.Doi: 10.1016/j.physa. 2013.10.003.他的型号 a。在线社交网络中基于人类个体和社会行为的谣言传播模型,收录于: Springer,2018。.和加拉姆的模型。无飞机五角大楼法国骗局案。统计数据。机械。它的应用。320 (2003) 571–580.Doi: 10.1016/S0378-4371(02)01582-0.<br />
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==== Independent cascades models ====<br />
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==== Independent cascades models ====<br />
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= = = 独立级联模型 = = = <br />
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==== Linear threshold models ====<br />
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==== Linear threshold models ====<br />
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= = = = 线性阈值模型 = = = <br />
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==== Energy model ====<br />
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==== Energy model ====<br />
<br />
= = = 能量模型 = = = <br />
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==== HISBmodel model ====<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?''.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
The HISBmodel is a rumor propagation model that can reproduce a trend of this phenomenon and provide indicators to assess the impact of the rumor to effectively understand the diffusion process and reduce its influence.<br />
The variety that exists in human nature makes their decision-making ability pertaining to spreading information unpredictable, which is the primary challenge to model such a complex phenomenon.<br />
Hence, this model considers the impact of human individual and social behaviors in the spreading process of the rumors.<br />
The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors.<br />
Therefore, it try to understand the behavior of individuals, as well as their social interactions in OSNs, and highlight their impact on the dissemination of rumors.<br />
Thus, the model, attempts to answer the following question: ``When does an individual spread a rumor? When does an individual accept rumors? In which OSN does this individual spread the rumors?.<br />
First, it proposes a formulation of individual behavior towards a rumor analog to damped harmonic motion, which incorporates the opinions of individuals in the propagation process.<br />
Furthermore, it establishes rules of rumor transmission between individuals.<br />
As a result, it presents the HISBmodel propagation process, where new metrics are introduced to accurately assess the impact of a rumor spreading through OSNs.<br />
<br />
该模型是一个谣言传播模型,可以再现这种现象的趋势,并提供评估谣言影响的指标,以有效地了解扩散过程和减少其影响。人性中存在的多样性使得他们传播信息的决策能力不可预测,这是对这样一个复杂现象建模的主要挑战。因此,该模型考虑了人类个体和社会行为对谣言传播过程的影响。该模型提出的方法与文献中的其他模型类似,更关注于个人如何传播谣言。因此,它试图了解个人的行为,以及他们在 osn 的社会互动,并突出其对谣言传播的影响。因此,该模型试图回答以下问题: “一个人什么时候散布谣言?”?一个人什么时候会接受谣言?这个人在哪个网站上散布谣言。首先,针对一类阻尼谐波运动,提出了一种个体行为的表述方法,该方法在传播过程中综合了个体的观点。此外,它还建立了个体间谣言传播的规则。因此,它提出了 HISBmodel 传播过程,其中引入了新的度量,以准确评估谣言通过 osn 传播的影响。<br />
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== References ==<br />
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== References ==<br />
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= = 参考文献 = =<br />
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<references /><br />
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[[Category:Social networks]]<br />
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Category:Social networks<br />
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分类: 社交网络<br />
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<small>This page was moved from [[wikipedia:en:Rumor spread in social network]]. Its edit history can be viewed at [[社交网络上的谣言传播/edithistory]]</small></noinclude><br />
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