On Equivalence of Likelihood Maximization of Stochastic Block Model and Constrained Nonnegative Matrix Factorization

2016/04/05 by Zhongyuan Zhang, Yujie Gai, Zhang, Zhong-Yuan +7
Computer Science · Physics and Astronomy · #Complex Network Analysis Techniques #Data Visualization and Analytics #FOS: Computer and information sciences #Opinion Dynamics and Social Influence #Social and Information Networks (cs.SI)

paper · pdf · doi:10.48550/arxiv.1604.01200

openalex publication_date 2016/04/05 · openalex created_date 2017/05/05 · openalex updated_date 2026/07/28

Abstract

Community structures detection in complex network is important for understanding not only the topological structures of the network, but also the functions of it. Stochastic block model and nonnegative matrix factorization are two widely used methods for community detection, which are proposed from different perspectives. In this paper, the relations between them are studied. The logarithm of likelihood function for stochastic block model can be reformulated under the framework of nonnegative matrix factorization. Besides the model equivalence, the algorithms employed by the two methods are different. Preliminary numerical experiments are carried out to compare the behaviors of the algorithms.

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