社交网络上的谣言传播

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模板:Multiple issues

Rumor is an important form of social communications, 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. 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. While the microscopic models are more interested more on the micro interactions between individuals.

Rumor is an important form of social communications, 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. 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. While the microscopic models are more interested more on the micro interactions between individuals.

谣言是社会交往的一种重要形式,谣言的传播在人类生活的各个方面都发挥着重要作用。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-肯德尔模型和 Maki-Thompson 模型。尤其是,我们可以把谣言看作是社交网络中的随机过程。而微观模型对个体间的微观相互作用更感兴趣。

Rumor propagation Models

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. By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.

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. By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.

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,人们提出了不同的研究方法。通过对现有文献的仔细研究,我们将这些著作分为宏观和微观两类。

Macroscopic models

The first category is mainly based on the Epidemic models [1] where the pioneering research engaging rumor propagation under these models started during the 1960s.

The first category is mainly based on the Epidemic models Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42. where the pioneering research engaging rumor propagation under these models started during the 1960s.

= = = 宏观模型 = = = 第一类主要基于流行病模型 Daley,d.j,和 Kendal,d.g。1965年随机传闻,j. Inst。数学应用1,第42页。在这些模型下,开创性的研究从事谣言传播开始于20世纪60年代。

Epidemic models

A standard model of rumor spreading was introduced by Daley and Kendall,[1]. 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:

A standard model of rumor spreading was introduced by Daley and Kendall,. 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:

= = = = = 流行病模型 = = = = = 一个谣言传播的标准模型是由戴利和肯德尔,。假设总共有 n 个人。网络中的这些人可以分为三类: 无知者、扩散者和窒息者,在下文中分别称为 s、 i 和 r:

  • I: people who are ignorant of the rumor;
  • S: people who actively spread the rumor;
  • R: people who have heard the rumor, but no longer are interested in spreading it.
  • I: people who are ignorant of the rumor;
  • S: people who actively spread the rumor;
  • R: people who have heard the rumor, but no longer are interested in spreading it.


  • i: 对谣言一无所知的人;
  • s: 积极散布谣言的人;
  • r: 听说过谣言但不再有兴趣散布谣言的人。

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.

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.

谣言通过传播者和人群中其他人的成对接触在人群中传播。任何一个两人一组的散布者都试图用谣言“感染”另一个人。在这种情况下,另一个人是无知的,他或她成为一个传播者。在另外两个案例中,参与会议的一方或双方都知道谣言已经被发现,并决定不再说出这个谣言,从而变成了窒息者。

One variant is the Maki-Thompson model.[2] 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.

[math]\displaystyle{ \begin{matrix}{}\\ S+I\xrightarrow{\alpha}2S \\{}\end{matrix} }[/math]

 

 

 

 

(1)

which says when a spreader meet an ignorant, the ignorant will become a spreader.
[math]\displaystyle{ \begin{matrix}{}\\ S+S\xrightarrow{\beta}S+R \\{}\end{matrix} }[/math]

 

 

 

 

(2)

which says when two spreaders meet with each other, one of them will become a stifler.
[math]\displaystyle{ \begin{matrix}{}\\ S+R\xrightarrow{\beta}2R \\{}\end{matrix} }[/math]

 

 

 

 

(3)

which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.

One variant is the Maki-Thompson model.Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall. 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.

which says when a spreader meet an ignorant, the ignorant will become a spreader.
which says when two spreaders meet with each other, one of them will become a stifler.
which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.

一种变体是 Maki-Thompson 模型。1973年数学模型和应用,重点在社会,生活和管理科学,普伦蒂斯霍尔。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,当一个摊铺机接触另一个摊铺机只有发起摊铺机成为一个硬条。因此,三种类型的相互作用可以发生在一定的速率。当前位置: 当一个传播者遇到一个无知者,无知者就会成为一个传播者。当两个伸展器相遇时,其中一个会变成条子。当一个传播者遇到一个硬条时,这个传播者就会失去传播谣言的兴趣,所以成为一个硬条。

Of course we always have conservation of individuals:

[math]\displaystyle{ N=I+S+R }[/math]

Of course we always have conservation of individuals:

N=I+S+R

当然,我们总是有个体守恒: : n = i + s + r

The change in each class in a small time interval is:

[math]\displaystyle{ \Delta S \approx - \Delta t \alpha IS/N }[/math]
[math]\displaystyle{ \Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}] }[/math]
[math]\displaystyle{ \Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}] }[/math]

The change in each class in a small time interval is:

\Delta S \approx - \Delta t \alpha IS/N
\Delta I \approx \Delta t [{\alpha IS \over N} - {\beta I^2 \over N} - {\beta IR \over N}]
\Delta R \approx \Delta t [{\beta I^2 \over N}+{\beta IR \over N}]

每个类在小时间间隔内的变化是: Delta s approx-Delta t alpha IS/n: Delta i approx Delta t [{ alpha IS over n }-{ beta i ^ 2 over n }-{ beta IR over n }] : Delta r approx Delta t [{ beta i ^ 2 over n } + { beta IR over n }]

Since we know [math]\displaystyle{ S }[/math], [math]\displaystyle{ I }[/math] and [math]\displaystyle{ R }[/math] sum up to [math]\displaystyle{ N }[/math], we can reduce one equation from the above, which leads to a set of differential equations using relative variable [math]\displaystyle{ x=I/N }[/math] and [math]\displaystyle{ y=S/N }[/math] as follows

[math]\displaystyle{ {dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y) }[/math]
[math]\displaystyle{ {dy \over dt} = - \alpha xy }[/math]

which we can write

[math]\displaystyle{ {dx \over dt} = (\alpha + \beta)xy - \beta x }[/math]
[math]\displaystyle{ {dy \over dt} = - \alpha xy }[/math]

Since we know S, I and R sum up to N, we can reduce one equation from the above, which leads to a set of differential equations using relative variable x=I/N and y=S/N as follows

{dx \over dt} = x \alpha y - \beta x^2 - \beta x(1-x-y)
{dy \over dt} = - \alpha xy

which we can write

{dx \over dt} = (\alpha + \beta)xy - \beta x
{dy \over dt} = - \alpha xy

由于我们知道 s,i 和 r 的和等于 n,我们可以从上面的一个方程出发,用相对变量 x = i/n 和 y = s/n 导出一组微分方程: { dx/dt } = x alpha y-beta x ^ 2-beta x (1-x-y) : { dy/dt } =-alpha xy,可以写成: { dx/dt } = (alpha + beta) xy-beta x: { dy/dt } =-xy

Compared with the ordinary SIR model, we see that the only difference to the ordinary SIR model is that we have a factor [math]\displaystyle{ \alpha + \beta }[/math] in the first equation instead of just [math]\displaystyle{ \alpha }[/math]. We immediately see that the ignorants can only decrease since [math]\displaystyle{ x,y\ge 0 }[/math] and [math]\displaystyle{ {dy \over dt}\le 0 }[/math]. Also, if

[math]\displaystyle{ R_0={\alpha +\beta \over \beta} \gt 1 }[/math]

which means

[math]\displaystyle{ {\alpha \over \beta}\gt 0 }[/math]

the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.

Compared with the ordinary SIR model, we see that the only difference to the ordinary SIR model is that we have a factor \alpha + \beta in the first equation instead of just \alpha. We immediately see that the ignorants can only decrease since x,y\ge 0 and {dy \over dt}\le 0. Also, if

R_0={\alpha +\beta \over \beta} >1

which means

{\alpha \over \beta}>0

the rumour model exhibits an “epidemic” even for arbitrarily small rate parameters.

与一般的 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 α + β,而不仅仅是 α。我们立即看到,无利润只能从 x,y ge 0和{ dy/dt } le 0开始减少。此外,如果: r _ 0 = { alpha + beta over beta } > 1,这意味着: { alpha over beta } > 0,即使在任意小的速率参数下,谣言模型也表现出“流行性”。

Epidemic models in social network

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]\displaystyle{ X_i(t) }[/math] to be the state of node i at time t. Then [math]\displaystyle{ X(t) }[/math] is a stochastic process on [math]\displaystyle{ 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]\displaystyle{ f }[/math] so that for [math]\displaystyle{ x }[/math] in [math]\displaystyle{ S }[/math],[math]\displaystyle{ f(x,i,j) }[/math] is when the state of network is [math]\displaystyle{ 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]\displaystyle{ y=f(x,i,j) }[/math], we try to find [math]\displaystyle{ P(x,y) }[/math]. If node i is in state I and node j is in state S, then [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ P(x,y)=\beta A_{ji}/k_i }[/math]. For all other [math]\displaystyle{ y }[/math], [math]\displaystyle{ P(x,y)=0 }[/math].
The procedure[3] on a network is as follows: 模板:Ordered list

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 X_i(t) to be the state of node i at time t. Then X(t) is a stochastic process on S=\{S,I,R\}^N. 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 f so that for x in S,f(x,i,j) is when the state of network is x, 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 y=f(x,i,j), we try to find P(x,y). If node i is in state I and node j is in state S, then P(x,y)=\alpha A_{ji}/k_i; if node i is in state I and node j is in state I, then P(x,y)=\beta A_{ji}/k_i; if node i is in state I and node j is in state R, then P(x,y)=\beta A_{ji}/k_i. For all other y, P(x,y)=0. The procedureBrockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University on a network is as follows:


= = = = 社会网络中的传染病模型 = = = = = 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 DTMC。假设我们有一个 n 个节点的网络,那么我们可以定义 x _ i (t)为时间 t 的节点 i 的状态。那么 x (t)是 s = { s,i,r } ^ n 上的随机过程。在某一时刻,某个节点 i 和节点 j 相互交互,然后其中一个节点将改变其状态。因此我们定义了函数 f,使得对于 s 中的 x,f (x,i,j)是当网络状态为 x 时,节点 i 和节点 j 相互作用,其中一个将改变其状态。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 y = f (x,i,j) ,我们尝试求 p (x,y)。如果节点 i 处于状态 i,节点 j 处于状态 s,则 p (x,y) = alpha a _ { ji }/k _ i; 如果节点 i 处于状态 i,节点 j 处于状态 i,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 p (x,y) = beta a _ { ji }/k _ i。对于所有其他 y,p (x,y) = 0。2011 Complex Networks and Systems,Lecture Notes,The procedureBrockmann,d. 2011 Complex Networks and Systems,Lecture Notes,on a network is followed: 《复杂网络与系统》 ,西北大学如下:

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.

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.

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。

Also we can compute the final number of people who once spread the news, this is given by
[math]\displaystyle{ r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} }[/math]
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]\displaystyle{ r_\infty }[/math] as a function of the rewiring probability [math]\displaystyle{ p }[/math].

Also we can compute the final number of people who once spread the news, this is given by r_\infty=1-e^{-({\alpha +\beta \over \beta})r_\infty} 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.

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。

Microscopic models

The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom." The known models in this category are the information cascade and the linear threshold models,[4] the energy model,[5] HISBmodel [6] and Galam's Model.[7]

The microscopic approaches attracted more attention in the individual's interaction: "who influenced whom." 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.

= = = 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.

Independent cascades models

Independent cascades models

= = 独立级联模型 = =

Linear threshold models

Linear threshold models

= = = 线性阈值模型 = =

Energy model

Energy model

= = 能量模型 = =

HISBmodel model

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. 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. The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors. 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. 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?. 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. Furthermore, it establishes rules of rumor transmission between individuals. 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.

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. 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. The HISBmodel proposes an approach that is parallel to other models in the literature and concerned more with how individuals spread rumors. 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. 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?. 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. Furthermore, it establishes rules of rumor transmission between individuals. 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.

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。

References

References

= 参考文献 =

  1. 1.0 1.1 Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.
  2. Maki, D.P. 1973 Mathematical Models and Applications, With Emphasis on Social, Life, and Management Sciences, Prentice Hall.
  3. Brockmann, D. 2011 Complex Networks and Systems, Lecture Notes, Northwestern University
  4. [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.
  5. 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.
  6. 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..
  7. 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.

Category:Social networks

分类: 社交网络


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