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Community Detection in Dynamic Networks: Equivalence Between Stochastic Blockmodels and Evolutionary Spectral Clustering
IEEE Transactions on Signal and Information Processing over Networks ( IF 3.0 ) Pub Date : 2021-01-18 , DOI: 10.1109/tsipn.2021.3052047
Abdullah Karaaslanl , Selin Aviyente

Community detection aims to identify densely connected groups of nodes in complex networks. Although a variety of methods have been proposed for community detection, the relationship between them is not well understood. Recently, researchers have shown the equivalence between modularity optimization and likelihood maximization in stochastic block models (SBMs) for static networks. Showing this equivalence is important for both understanding the different community detection methods and selecting the hyperparameters in the different algorithms in a more principled way. In this paper, we extend this equivalence for dynamic community detection algorithms. In particular, we show the equivalence of evolutionary spectral clustering to a variant of dynamic stochastic blockmodel. For this purpose, we first introduce a novel dynamic SBM where the evolution of communities over time is modeled with pairwise Markov random fields. We then show that the log-posterior of the proposed model is equivalent to the quality function of evolutionary spectral clustering. This equivalence is used to determine the forgetting factor in evolutionary spectral clustering and to develop two new algorithms for dynamic community detection. Compared to original evolutionary spectral clustering, the forgetting factor is time-dependent and derived directly from the parameters of the proposed dynamic SBM. The proposed algorithms are shown to be superior to state-of-the-art dynamic community detection methods for both simulated and real-world dynamic networks.

中文翻译:

动态网络中的社区检测:随机块模型与进化谱聚类之间的等效性

社区检测旨在识别复杂网络中密集连接的节点组。尽管已经提出了多种方法来进行社区检测,但是它们之间的关系还不是很清楚。最近,研究人员显示了静态网络的随机块模型(SBM)中的模块化优化和似然最大化之间的等效性。展示这种等效性对于理解不同的社区检测方法以及以更原则的方式在不同算法中选择超参数都非常重要。在本文中,我们将这种等效性扩展到动态社区检测算法。特别是,我们展示了进化频谱聚类与动态随机模块模型的等效形式。以此目的,我们首先介绍一种新颖的动态SBM,其中使用配对的马尔可夫随机场对社区随时间的演变进行建模。然后,我们表明,所提出模型的对数后验等效于演化谱聚类的质量函数。这种等效性用于确定进化谱聚类中的遗忘因子,并开发两种用于动态社区检测的新算法。与原始的进化谱聚类相比,遗忘因子与时间有关,并且直接从所提出的动态SBM的参数中得出。结果表明,对于模拟和现实世界的动态网络,所提出的算法均优于最新的动态社区检测方法。然后,我们表明,所提出模型的对数后验等效于演化谱聚类的质量函数。这种等效性用于确定进化谱聚类中的遗忘因子,并开发两种用于动态社区检测的新算法。与原始的进化谱聚类相比,遗忘因子与时间有关,并且直接从所提出的动态SBM的参数中得出。结果表明,对于模拟和现实世界的动态网络,所提出的算法均优于最新的动态社区检测方法。然后,我们表明,所提出模型的对数后验等效于演化谱聚类的质量函数。这种等效性用于确定进化谱聚类中的遗忘因子,并为动态社区检测开发两种新算法。与原始的进化谱聚类相比,遗忘因子与时间有关,并且直接从所提出的动态SBM的参数中得出。结果表明,对于模拟和现实世界的动态网络,所提出的算法均优于最新的动态社区检测方法。这种等效性用于确定进化谱聚类中的遗忘因子,并开发两种用于动态社区检测的新算法。与原始的进化谱聚类相比,遗忘因子与时间有关,并且直接从所提出的动态SBM的参数中得出。结果表明,对于模拟和现实世界的动态网络,所提出的算法均优于最新的动态社区检测方法。这种等效性用于确定进化谱聚类中的遗忘因子,并开发两种用于动态社区检测的新算法。与原始的进化谱聚类相比,遗忘因子与时间有关,并且直接从提出的动态SBM的参数中得出。结果表明,对于模拟和现实世界的动态网络,所提出的算法均优于最新的动态社区检测方法。
更新日期:2021-02-05
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