Open Access
February 2020 Spectral and matrix factorization methods for consistent community detection in multi-layer networks
Subhadeep Paul, Yuguo Chen
Ann. Statist. 48(1): 230-250 (February 2020). DOI: 10.1214/18-AOS1800


We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general theme, these “intermediate fusion” methods involve obtaining a low column rank matrix by optimizing an objective function and then using the columns of the matrix for clustering. However, the theoretical properties of these methods remain largely unexplored. In the absence of statistical guarantees on the objective functions, it is difficult to determine if the algorithms optimizing the objectives will return good community structures. We investigate the consistency properties of the global optimizer of some of these objective functions under the multi-layer stochastic blockmodel. For this purpose, we derive several new asymptotic results showing consistency of the intermediate fusion techniques along with the spectral clustering of mean adjacency matrix under a high dimensional setup, where the number of nodes, the number of layers and the number of communities of the multi-layer graph grow. Our numerical study shows that the intermediate fusion techniques outperform late fusion methods, namely spectral clustering on aggregate spectral kernel and module allegiance matrix in sparse networks, while they outperform the spectral clustering of mean adjacency matrix in multi-layer networks that contain layers with both homophilic and heterophilic communities.


Download Citation

Subhadeep Paul. Yuguo Chen. "Spectral and matrix factorization methods for consistent community detection in multi-layer networks." Ann. Statist. 48 (1) 230 - 250, February 2020.


Received: 1 April 2017; Revised: 1 December 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196537
MathSciNet: MR4065160
Digital Object Identifier: 10.1214/18-AOS1800

Primary: 62F12 , 62H30
Secondary: 15A23 , 90B15

Keywords: Community detection , consistency , co-regularized spectral clustering , multi-layer networks , multi-layer stochastic block model , orthogonal linked matrix factorization

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 1 • February 2020
Back to Top