Degree-Corrected Joint Matrix Factorization for Multilayer Community Detection

2026-10-01

AI Summary

This study addresses the challenge of community detection in multiplex networks arising from node degree heterogeneity and inter-layer structural discrepancies. We propose a novel method based on non-negative symmetric matrix tri-factorization that constrains communities to be shared and disjoint across layers while permitting each layer to retain distinct connectivity patterns and degree distributions. By integrating a multiplex degree-corrected stochastic block model (MDCBM), our approach overcomes the limitations of traditional methods restricted to globally consistent structures, enabling flexible joint modeling of local and global structural variations alongside degree correction. Experimental results demonstrate that the proposed method reliably detects communities across diverse scenarios, significantly outperforming state-of-the-art approaches constrained by rigid structural assumptions.

Abstract

Multilayer networks allow the modeling of interactions between the same entities across different contexts, such as temporal observations, varying settings, or interactions of different types. The goal of community detection in multilayer networks is to identify groups of nodes exhibiting similar connectivity patterns, which may vary across layers. We propose a method based on a joint nonnegative symmetric matrix trifactorization for community detection in multilayer networks, where each graph is approximated by a nonnegative symmetric matrix trifactorization. Our approach enforces constraints on the factor matrices so that communities are disjoint and shared across layers, while allowing each layer to have its own connectivity patterns and node degrees. This flexibility enables the model to capture both local and global structural variations across layers. We also develop an algorithm to efficiently solve this problem. We evaluate multilayer community detection methods using the multilayer degree-corrected stochastic block model (MDCBM), a flexible framework for generating realistic multilayer graphs with heterogeneous degrees and varying connectivity patterns. Experiments show that our method reliably detects communities across diverse regimes, whereas existing state-of-the-art approaches are often limited by restrictive structural assumptions.

Problem

• Multilayer networks
• Community detection
• Degree heterogeneity
• Matrix factorization

Innovation

• Multilayer Community Detection
• Joint Matrix Trifactorization
• Degree-Corrected
• Nonnegative Matrix Factorization
• Stochastic Block Model