Multi-Graph Contrastive Learning for Community Detection in Multi-Layer Networks

Multi-layer networks effectively describe and model complex systems in nature and society, with each layer corresponding to a different type of interaction relationship. Community detection in multi-layer networks aims to identify modules with strong connectivity in all layers, thus revealing interactions in complex systems. However, current algorithms have been criticized for failing to adequately quantify the underlying structure and extract discriminative features. To tackle these issues, we propose
M
ulti-graph
C
ontrastive
L
earning with
C
onsistency and
D
iversity for clustering of multi-layer networks (MCLCD), which includes feature extraction, feature decomposition, contrastive learning, and feature fusion. Specifically, MCLCD utilizes joint nonnegative matrix decomposition to extract features from each layer of the network. To quantify the underlying structure, the features are decomposed into consistent and diverse parts. The former characterizes consistency in each layer, reflecting the community structure, while the latter models the specificity and noise in each layer. Then, MCLCD performs multi-graph contrastive learning with negative samples constructed from neighbor information, which enhances the discriminative properties of consistent parts. These parts are integrated into an objective function and an optimization process is derived. Extensive experiments on both artificial networks and real-world networks show that MCLCD surpasses state-of-the-art methods in terms of various metrics, highlighting the excellence of our proposed approach.