Detecting memberships in multiplex networks via nonnegative matrix factorization and tensor decomposition

Abstract

Listen

Translate article

Abstract Multiplex networks provide a powerful data structure for capturing diverse relationships among nodes, and the challenge of community detection within these networks has recently attracted considerable attention. We propose a general and flexible generative model—the Mixed Membership Multilayer Stochastic Block Model (MixMSBM), in which layers with meaningful similarities are grouped together. Within each layer group, the layers share the same mixed membership assignments of nodes to communities, but with distinct community link probability matrices. To address this, we developed NMFTD, a joint clustering approach, to identify cohesive layer groups and determine the mixed memberships of nodes within them. Our method first clusters the layers using matrix factorization with graph regularization, followed by a tensor decomposition strategy enhanced by a corner-finding algorithm to uncover the nodes' mixed memberships in each group. The proposed method is asymptotically consistent, and its effectiveness is validated through experiments on synthetic and real-world multilayer networks. The results show that NMFTD exhibits robustness across various parameter settings, outperforming or competing closely with other methods.