A fast algorithm for integrative community detection of multi‐layer networks. Issue 1 (25th March 2021)

• Record Type: Journal Article
• Authors: Wang, Jiangzhou; Guo, Jianhua; Liu, Binghui
• Is Part Of: Stat. Volume 10:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-25
• Subjects: community detection -- multi‐layer networks -- pseudo‐likelihood -- stochastic block models -- twitter networks; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.348
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : Multi‐layer networks are often used to represent multiple types of relationships between nodes in network studies. In this paper, we investigate the community detection problem in multi‐layer networks. Specifically, we consider the multi‐layer stochastic block model (MLSBM), which assumes that the community memberships are shared across all network layers, while other model parameters can be different between different layers. Variational methods have been developed to fit the MLSBM, but they do not scale well to very large networks. Inspired by the iterative pseudo‐likelihood maximization strategy for single networks, we develop a pseudo‐likelihood based algorithm to fit the MLSBM and estimate the community labels, and we also extend the proposed algorithm to the degree‐corrected case to deal with degree heterogeneity. The proposed algorithms are fast and can cope with multi‐layer networks with up to millions of nodes. The advantages of the proposed methods in both community detection and computational efficiency are demonstrated by numerical studies.