优先链接

本词条由Ryan初步翻译。由Fernando审校。

"Yule process" redirects here. For the type of birth process, see Simple birth process.

A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names "Yule process", "cumulative advantage", "the rich get richer", and, less correctly, the "Matthew effect". They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions.

A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who are already wealthy receive more than those who are not. "Preferential attachment" is only the most recent of many names that have been given to such processes. They are also referred to under the names "Yule process", "cumulative advantage", "the rich get richer", and, less correctly, the "Matthew effect". They are also related to Gibrat's law. The principal reason for scientific interest in preferential attachment is that it can, under suitable circumstances, generate power law distributions.

优先链接 Preferential Attachment过程是一类过程，在这类过程中，某些量(通常是某种形式的财富或信贷)是根据一些人或事物已经拥有的量来分配的，从而使那些已经富有的人比那些不富有的人得到更多。”优先链接”是描述该过程的众多名称中最贴近其本质含义的名称。它还被称为“Yule过程”、“可积累的优势”、“富人越来越富” ，以及不那么确切的“马太效应”。它们也与吉布拉定律有关。优先链接之所以受到科学家的关注，主要是因为它能在适当的条件下产生幂律分布 Power Law Distributions。

Definition 定义

A preferential attachment process is a stochastic urn process, meaning a process in which discrete units of wealth, usually called "balls", are added in a random or partly random fashion to a set of objects or containers, usually called "urns". A preferential attachment process is an urn process in which additional balls are added continuously to the system and are distributed among the urns as an increasing function of the number of balls the urns already have. In the most commonly studied examples, the number of urns also increases continuously, although this is not a necessary condition for preferential attachment and examples have been studied with constant or even decreasing numbers of urns.

A preferential attachment process is a stochastic urn process, meaning a process in which discrete units of wealth, usually called "balls", are added in a random or partly random fashion to a set of objects or containers, usually called "urns". A preferential attachment process is an urn process in which additional balls are added continuously to the system and are distributed among the urns as an increasing function of the number of balls the urns already have. In the most commonly studied examples, the number of urns also increases continuously, although this is not a necessary condition for preferential attachment and examples have been studied with constant or even decreasing numbers of urns.

优先链接过程是一个随机瓮过程 Stochastic Urn Process，也就是说离散的财富单位(通常称为“球”)，以随机或部分随机的方式添加到一组物体或容器(通常称为“瓮”)。优先链接过程是一个瓮过程，在这个过程中，额外的球被不断地添加到系统中，并作为瓮中已有球数的递增函数分配到瓮中。尽管在最常研究的例子中，翁的数量也在不断增加，但是这不是优先链接的必要条件，有一些研究的例子伴随着翁数量不变甚至减少的现象。

A classic example of a preferential attachment process is the growth in the number of species per genus in some higher taxon of biotic organisms. New genera ("urns") are added to a taxon whenever a newly appearing species is considered sufficiently different from its predecessors that it does not belong in any of the current genera. New species ("balls") are added as old ones speciate (i.e., split in two) and, assuming that new species belong to the same genus as their parent (except for those that start new genera), the probability that a new species is added to a genus will be proportional to the number of species the genus already has. This process, first studied by Yule, is a linear preferential attachment process, since the rate at which genera accrue new species is linear in the number they already have.

A classic example of a preferential attachment process is the growth in the number of species per genus in some higher taxon of biotic organisms. New genera ("urns") are added to a taxon whenever a newly appearing species is considered sufficiently different from its predecessors that it does not belong in any of the current genera. New species ("balls") are added as old ones speciate (i.e., split in two) and, assuming that new species belong to the same genus as their parent (except for those that start new genera), the probability that a new species is added to a genus will be proportional to the number of species the genus already has. This process, first studied by Yule, is a linear preferential attachment process, since the rate at which genera accrue new species is linear in the number they already have.

优先链接过程的一个典型例子是生物有机体的某些高级分类单元中每个属的物种数量的增长。每当一个新出现的物种被认为与其祖先完全不同，不属于任何一个现有属时，新属(“urns”)就被添加到分类单元中。新物种(“球”)加入的时候旧物种发生演变(即一分为二)，如果认为新物种与其亲本属于同一属(除外它们本身是新属)，那么新物种加入该属的概率将与该属已有的物种数量成正比。这个首先被Yule研究的过程，就是一个线性优先链接的过程，因为新物种的繁殖率与其已经拥有的数量成线性关系。

Linear preferential attachment processes in which the number of urns increases are known to produce a distribution of balls over the urns following the so-called Yule distribution. In the most general form of the process, balls are added to the system at an overall rate of m new balls for each new urn. Each newly created urn starts out with k₀ balls and further balls are added to urns at a rate proportional to the number k that they already have plus a constant a > −k₀. With these definitions, the fraction P(k) of urns having k balls in the limit of long time is given by

Linear preferential attachment processes in which the number of urns increases are known to produce a distribution of balls over the urns following the so-called Yule distribution. In the most general form of the process, balls are added to the system at an overall rate of m new balls for each new urn. Each newly created urn starts out with k₀ balls and further balls are added to urns at a rate proportional to the number k that they already have plus a constant a > −k₀. With these definitions, the fraction P(k) of urns having k balls in the limit of long time is given by

翁的数量增加的线性优先链接过程，会在翁中按照所谓的Yule分布产生球的分布。在最一般形式的过程中，球添加到系统中的整体速率是每个瓮中添加m个新球。每个新创建的瓮都以 k₀ 个球开始，然后新球被不断地添加到瓮中，其速度与瓮的数量k加常数 a > >k₀成正比。利用这些定义，可以给出长时极限下具有k个球的瓮的分数P(k):

[math]\displaystyle{ P(k)={\mathrm{B}(k+a,\gamma)\over\mathrm{B}(k_0+a,\gamma-1)}, }[/math]

[math]\displaystyle{ P(k)={\mathrm{B}(k+a,\gamma)\over\mathrm{B}(k_0+a,\gamma-1)}, }[/math]

for k ≥ k₀ (and zero otherwise), where B(x, y) is the Euler beta function:

for k ≥ k₀ (and zero otherwise), where B(x, y) is the Euler beta function:

对于k ≥ k₀(否则为0) ，其中 b (x，y)是 Euler beta 函数:

[math]\displaystyle{ \mathrm{B}(x,y)={\Gamma(x)\Gamma(y)\over\Gamma(x+y)}, }[/math]

[math]\displaystyle{ \mathrm{B}(x,y)={\Gamma(x)\Gamma(y)\over\Gamma(x+y)}, }[/math]

with Γ(x) being the standard gamma function, and

with Γ(x) being the standard gamma function, and

(x)是标准伽马函数，并且

[math]\displaystyle{ \gamma=2 + {k_0 + a\over m}. }[/math]

[math]\displaystyle{ \gamma=2 + {k_0 + a\over m}. }[/math]

The beta function behaves asymptotically as B(x, y) ~ x^−y for large x and fixed y, which implies that for large values of k we have

The beta function behaves asymptotically as B(x, y) ~ x^−y for large x and fixed y, which implies that for large values of k we have

对于较大的x和固定的y，β函数表现为B(x, y) ~ x^−y，这意味着对于k的大值，我们有一个渐近的β函数

[math]\displaystyle{ P(k) \propto k^{-\gamma}. }[/math]

[math]\displaystyle{ P(k) \propto k^{-\gamma}. }[/math]

In other words, the preferential attachment process generates a "long-tailed" distribution following a Pareto distribution or power law in its tail. This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the preferential attachment process is a leading candidate mechanism to explain this behavior. Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities, the wealth of extremely wealthy individuals, the number of citations received by learned publications, and the number of links to pages on the World Wide Web.

In other words, the preferential attachment process generates a "long-tailed" distribution following a Pareto distribution or power law in its tail. This is the primary reason for the historical interest in preferential attachment: the species distribution and many other phenomena are observed empirically to follow power laws and the preferential attachment process is a leading candidate mechanism to explain this behavior. Preferential attachment is considered a possible candidate for, among other things, the distribution of the sizes of cities, the wealth of extremely wealthy individuals, and the number of links to pages on the World Wide Web.

换句话说，优先链接过程在其尾部产生一个遵循帕累托分布 Pareto Distribution或幂定律 Power Law的“长尾”分布 Long-Tailed Distribution。这是历史上人们对优先链接感兴趣的主要原因: 经过实际的观察，物种分布和许多其他现象都遵循幂律分布，而优先链接过程是解释这种行为的主要候选机制。它还可能解释如城市规模的分布，大富豪的财富 the number of citations received by learned publications,，以及万维网网页的链接数量等问题。

The general model described here includes many other specific models as special cases. In the species/genus example above, for instance, each genus starts out with a single species (k₀ = 1) and gains new species in direct proportion to the number it already has (a = 0), and hence P(k) = B(k, γ)/B(k₀, γ − 1) with γ=2 + 1/m. Similarly the Price model for scientific citations corresponds to the case k₀ = 0, a  = 1 and the widely studied Barabási-Albert model corresponds to k₀ = m, a = 0.

The general model described here includes many other specific models as special cases. In the species/genus example above, for instance, each genus starts out with a single species (k₀ = 1) and gains new species in direct proportion to the number it already has (a = 0), and hence P(k) = B(k, γ)/B(k₀, γ − 1) with γ=2 + 1/m. Similarly the Price model for scientific citations corresponds to the case k₀ = 0, a  = 1 and the widely studied Barabási-Albert model corresponds to k₀ = m, a = 0.

这里描述的一般模型包括许多作为特例的其他特定模型。例如，在上面的种属例子中，每个属以一个单一的种(k₀ = 1)开始，并且获得的新种正比于它已有的种的数量(a = 0) ，因此P(k) = B(k, γ)/B(k₀, γ − 1)，γ=2 + 1/m. 。类似地，科学引文的价格模型 Price Model 对应于k₀ = 0，a  = 1 ，而广泛研究的Barabási-Albert 模型对应于 k₀ = m, a = 0.。

Preferential attachment is sometimes referred to as the Matthew effect, but the two are not precisely equivalent. The Matthew effect, first discussed by Robert K. Merton, is named for a passage in the biblical Gospel of Matthew: "For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him." (Matthew 25:29, New International Version.) The preferential attachment process does not incorporate the taking away part. This point may be moot, however, since the scientific insight behind the Matthew effect is in any case entirely different. Qualitatively it is intended to describe not a mechanical multiplicative effect like preferential attachment but a specific human behavior in which people are more likely to give credit to the famous than to the little known. The classic example of the Matthew effect is a scientific discovery made simultaneously by two different people, one well known and the other little known. It is claimed that under these circumstances people tend more often to credit the discovery to the well-known scientist. Thus the real-world phenomenon the Matthew effect is intended to describe is quite distinct from (though certainly related to) preferential attachment.

Preferential attachment is sometimes referred to as the Matthew effect, but the two are not precisely equivalent. The Matthew effect, first discussed by Robert K. Merton, is named for a passage in the biblical Gospel of Matthew: "For everyone who has will be given more, and he will have an abundance. Whoever does not have, even what he has will be taken from him." (Matthew 25:29, New International Version.) The preferential attachment process does not incorporate the taking away part. This point may be moot, however, since the scientific insight behind the Matthew effect is in any case entirely different. Qualitatively it is intended to describe not a mechanical multiplicative effect like preferential attachment but a specific human behavior in which people are more likely to give credit to the famous than to the little known. The classic example of the Matthew effect is a scientific discovery made simultaneously by two different people, one well known and the other little known. It is claimed that under these circumstances people tend more often to credit the discovery to the well-known scientist. Thus the real-world phenomenon the Matthew effect is intended to describe is quite distinct from (though certainly related to) preferential attachment.

优先链接有时被称为马太效应，但两者并不完全等同。马太效应，最早由罗伯特·金·莫顿讨论，是根据《圣经》中的一段马太福音命名的: 凡有的，还要加给他，叫他有余；凡没有的，连他所有的也要夺去。(马太福音25:29，新国际版)。优先链接过程并不包括夺走的部分。但是这一说法可能没有意义，因为马太效应背后的科学见解无论如何都是不一样的。定性地说，它并不是像如优先链接一样在描述一种机械的乘法效应，而是在描述一种特定的人类行为。在这种行为中，人们更有可能给归功于名人而不是归功于小透明。马太效应的经典例子是：两个不同的人同时做出了某项科学发现，其中一个人十分有名，另一个人则鲜为人知；据称，在这种情况下，人们往往更倾向于将这一发现归功于著名的科学家。因此，马太效应所要描述的现实景象与优先链接是截然不同的(虽然肯定与优先链接有关)。

History 历史

The first rigorous consideration of preferential attachment seems to be that of Udny Yule in 1925, who used it to explain the power-law distribution of the number of species per genus of flowering plants. The process is sometimes called a "Yule process" in his honor. Yule was able to show that the process gave rise to a distribution with a power-law tail, but the details of his proof are, by today's standards, contorted and difficult, since the modern tools of stochastic process theory did not yet exist and he was forced to use more cumbersome methods of proof.

The first rigorous consideration of preferential attachment seems to be that of Udny Yule in 1925, who used it to explain the power-law distribution of the number of species per genus of flowering plants. The process is sometimes called a "Yule process" in his honor. Yule was able to show that the process gave rise to a distribution with a power-law tail, but the details of his proof are, by today's standards, contorted and difficult, since the modern tools of stochastic process theory did not yet exist and he was forced to use more cumbersome methods of proof.

1925年，那时的Udny Yule是第一个对优先链接进行严谨考量的人，他用它来解释被子植物属中物种数量的幂律分布。为了纪念他，这个过程有时被称为“Yule过程”。Yule能够证明这个过程产生了一个带有幂律尾巴的分布，但是他的证明的细节，按照今天的标准，是曲折和晦涩的，因为现代的随机过程理论工具当时还不存在，他被迫使用更加繁琐的证明方法。

Most modern treatments of preferential attachment make use of the master equation method, whose use in this context was pioneered by Simon in 1955, in work on the distribution of sizes of cities and other phenomena.

Most modern treatments of preferential attachment make use of the master equation method, whose use in this context was pioneered by Simon in 1955, in work on the distribution of sizes of cities and other phenomena.

大多数现代优先链接的处理方法都使用了主方程方法 Master Equation Method，这种方法在1955年由 Simon 首创，用于研究城市规模和其他现象的分布。

The first application of preferential attachment to learned citations was given by Price in 1976. (He referred to the process as a "cumulative advantage" process.) His was also the first application of the process to the growth of a network, producing what would now be called a scale-free network. It is in the context of network growth that the process is most frequently studied today. Price also promoted preferential attachment as a possible explanation for power laws in many other phenomena, including Lotka's law of scientific productivity and Bradford's law of journal use.

The first application of preferential attachment to learned citations was given by Price in 1976. (He referred to the process as a "cumulative advantage" process.) His was also the first application of the process to the growth of a network, producing what would now be called a scale-free network. It is in the context of network growth that the process is most frequently studied today. Price also promoted preferential attachment as a possible explanation for power laws in many other phenomena, including Lotka's law of scientific productivity and Bradford's law of journal use.

普赖斯于1976年首次将优先链接应用于学术引文。(他把这个过程称为“优势累积” Cumulative Advantage过程。)他也是第一个将这一过程应用于网络发展的人，他创造了现在所谓的无标度网络 Scale-Free Network。正是在网络增长的背景下，这一过程在今天得到了最频繁的研究。普莱斯还将优先链接作为许多其他现象中幂定律的可能解释，包括洛特卡的科学生产力定律和布拉德福德的期刊使用定律。

The application of preferential attachment to the growth of the World Wide Web was proposed by Barabási and Albert in 1999. Barabási and Albert also coined the name "preferential attachment" by which the process is best known today and suggested that the process might apply to the growth of other networks as well. For growing networks, the precise functional form of preferential attachment can be estimated by maximum likelihood estimation.

The application of preferential attachment to the growth of the World Wide Web was proposed by Barabási and Albert in 1999.

1999年，Barabási 和 Albert 提出了优先链接在万维网发展中的应用。

See also 另请参阅

• Assortative mixing

关联矩阵

• BA model

BA模型

• Bose–Einstein condensation: a network theory approach

玻色-爱因斯坦凝聚：一种网络理论方法

• Capital accumulation

资本积累

• Chinese restaurant process

中餐厅过程

• Complex network

复杂网络

• Double jeopardy (marketing)

双重危险（营销）

• Link-centric preferential attachment

以链接为中心的优先链接

• Matthew effect (sociology)

马太效应（社会学）

• Pitman–Yor process

Pitman-Yor过程

• Power law

幂定律

• Price's model

价格模型

• Proof of stake

权益证明

• Simon model

西蒙模型

• Stochastic processes

随机过程

• Wealth condensation

财富集聚

• Yule–Simon distribution

Yule-Simon 分布

• Bibliogram

书目图

References 引用

Category:Stochastic processes

类别: 随机过程

This page was moved from wikipedia:en:Preferential attachment. Its edit history can be viewed at 优先链接/edithistory