High-order connectivity patterns-incorporated contrastive learning for community detection

Community detection is a key hot issue in the area of complex network analysis. With good interpretability, non-negative matrix factorization (NMF) is often used to build a community detector. However, most NMF-based methods only focus on the low-order topology represented by the adjacency matrix, ignoring the key role of high-order proximity and motif structure in network connection patterns. Moreover, most existing NMF-based community detectors are limited by the linear shallow framework and are difficult to effectively capture the nonlinear characteristics of non-Euclidean networks. To tackle those issues, this study proposes a novel High-order Connectivity Patterns-incorporated Contrastive Learning (HCPCL) model for community detection with four ideas: a) incorporating high-order proximities into the original network via a well-designed network enhancement scheme to strengthen its structural information; b) constructing a high-order network based on motifs to represent the features of motif structures; c) leveraging the concept of contrastive learning to deeply fuse two kinds of high-order connectivity information and comprehensively extract local and global characteristics; and d) boosting an NMF-based representation learning framework by a graph attention autoencoder. Empirical studies on six real networks validate the effectiveness of the proposed HCPCL-based community detector.