模块网络随机块模型的渐近分析及其算法应用
Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
摘要：
在本文中，我们扩展了我们以前的工作随机块模型，社会和生物网络的一个常用的生成模型，以及从网络的拓扑结构推断功能组或社区的问题。我们使用统计物理的腔方法来获得相图的渐近精确分析。我们详细描述了社区检测问题的可检测性/不可检测性相变和易/难相变的性质。我们的分析自然地转化为用于以最佳方式推断节点的组成员资格的置信传播算法，即，最大化与底层组成员的重叠，并学习块模型的底层参数。最后，我们将该算法应用到两个现实世界的网络的例子，并讨论其性能。
英文摘要：
In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We describe in detail properties of the detectability/undetectability phase transition and the easy/hard phase transition for the community detection problem. Our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way, i.e., that maximizes the overlap with the underlying group memberships, and learning the underlying parameters of the block model. Finally, we apply the algorithm to two examples of real-world networks and discuss its performance.
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