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arXiv 1409.3207cs.SIphysics.soc-ph
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谱社区检测中的相变

Phase Transitions in Spectral Community Detection

Pin-Yu Chen, Alfred O. Hero

AI总结:

本文研究两社区经随机外部边连接时的谱聚类检测问题,利用随机矩阵理论刻画连接概率临界值处的突变相变并推导其上下界。

摘要:

考虑一个由两个子网络(社区)组成、并通过若干外部边相连的网络。给定网络拓扑,社区检测问题可表述为一个图划分问题,其目标是识别作为图割的外部边,从而将这两个子网络分开。本文考虑一个一般模型,其中两个任意连接的子网络通过随机外部边相连。利用随机矩阵理论和集中不等式,我们表明,当通过谱聚类执行社区检测时,随着随机外部边连接概率的变化,存在一个突变的相变。具体而言,在随机外部边连接概率的某个临界值附近,社区检测性能会从近乎完美的可检测性转变为低可检测性。我们推导了该临界值的上界和下界,并表明当两个子网络规模相同时,这些界限彼此相等。利用模拟数据和实验数据,我们展示了如何根据经验估计这些界限,以验证任何已发现社区的检测可靠性。

英文摘要:

Consider a network consisting of two subnetworks (communities) connected by some external edges. Given the network topology, the community detection problem can be cast as a graph partitioning problem that aims to identify the external edges as the graph cut that separates these two subnetworks. In this paper, we consider a general model where two arbitrarily connected subnetworks are connected by random external edges. Using random matrix theory and concentration inequalities, we show that when one performs community detection via spectral clustering there exists an abrupt phase transition as a function of the random external edge connection probability. Specifically, the community detection performance transitions from almost perfect detectability to low detectability near some critical value of the random external edge connection probability. We derive upper and lower bounds on the critical value and show that the bounds are equal to each other when two subnetwork sizes are identical. Using simulated and experimental data we show how these bounds can be empirically estimated to validate the detection reliability of any discovered communities.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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