翻訳と辞書 Words near each other ・ Stoborough Green ・ Stobrawa ・ Stobrawa (potato) ・ Stobrawa Landscape Park ・ Stobrawa, Opole Voivodeship ・ Stobreč ・ Stobrum ・ Stobswell ・ Stoby ・ Stocaigh ・ Stoccareddo ・ Stocco ・ Stoch ・ Stochastic ・ Stochastic approximation ・ Stochastic block model ・ Stochastic calculus ・ Stochastic cellular automaton ・ Stochastic computing ・ Stochastic context-free grammar ・ Stochastic control ・ Stochastic cooling ・ Stochastic differential equation ・ Stochastic diffusion search ・ Stochastic discount factor ・ Stochastic dominance ・ Stochastic drift ・ Stochastic electrodynamics ・ Stochastic Empirical Loading and Dilution Model ・ Stochastic equicontinuity Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stochastic block model ： ウィキペディア英語版 Stochastic block model The stochastic block model is a generative model for random graphs. This model tends to produce graphs containing ''communities'', subsets characterized by being connected with one another with particular edge densities. For example, edges may be more common within communities than between communities. The stochastic block model is important in statistics, machine learning, and network science, where it serves as a useful benchmark for the task of recovering community structure in graph data. == Definition == The stochastic block model takes the following parameters: * The number $n$ of vertices; * a partition of the vertex set $\backslash$ into disjoint subsets $C\_1,\backslash ldots,C\_r$, called ''communities''; * a symmetric $r\; \backslash times\; r$ matrix $P$ of inter-community edge probabilities. The edge set is then sampled at random as follows: any two vertices $u\; \backslash in\; C\_i$ and $v\; \backslash in\; C\_j$ are connected by an edge with probability $P\_$. == Special cases == If the probability matrix is a constant, in the sense that $P\_\; =\; p$ for all $i,j$, then the result is the Erdős–Rényi model $G(n,p)$. This case is degenerate—the partition into communities becomes irrelevant—but it illustrates a close relationship to the Erdős–Rényi model. The ''planted partition model'' is the special case that the values of the probability matrix $P$ are a constant $p$ on the diagonal and another constant $q$ off the diagonal. Thus two vertices within the same community share an edge with probability $p$, while two vertices in different communities share an edge with probability $q$. Sometimes it is this restricted model that is called the stochastic block model.〔 The case where $p\; >\; q$ is called an ''assortative'' model, while the case is called ''dissortative''. Returning to the general stochastic block model, a model is called ''strongly assortative'' if $P\_\; >\; P\_$ whenever $j\; \backslash neq\; k$: all diagonal entries dominate all off-diagonal entries. A model is called ''weakly assortative'' if $P\_\; >\; P\_$ whenever $i\; \backslash neq\; j$: each diagonal entry is only required to dominate the rest of its own row and column.〔 ''Dissortative'' forms of this terminology exist, by reversing all inequalities. Algorithmic recovery is often easier against block models with assortative or dissortative conditions of this form.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stochastic block model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.