Enhancing NMF-Based Community Detection via A Higher-Order Proximity-Incorporated Graph Attention Autoencoder

Community detection reveals the organizational patterns of complex networks. With good interpretability, non-negative matrix factorization (NMF) approaches are often used for this task. However, their linearity limits the performance of community detection on networks with complex, sparse, and diverse structures. As graph neural networks (GNNs) have strong nonlinear representation power, combining NMF with GNNs can overcome this limitation. However, a GNN model generally faces the issue of over-smoothing and struggles to explicitly use higher-order proximity (HOP) among nodes. To address this issue, this paper proposes HNG, a HOP-enhanced nonlinear NMF approach for community detection, with three modules: HOP-incorporated network enhancement, graph attention autoencoder (GAAE), and NMF. It first leverages HOP explicitly to better characterize the community structure for the facility of community detection, and then applies a nonlinear NMF improved via a GAAE for accurate community detection. Experimental results on six real networks show that HNG significantly outperforms state-of-the-art methods in achieving community detection accuracy gain.