Constrained deep nonnegative matrix factorization with graph convolutional networks for unsupervised community detection

Abstract

Community detection is a key task for revealing functional organization in complex networks. Graph neural networks (GNNs) capture non-linear relationships but often suffer from over-smoothing as layers increase. Deep nonnegative matrix factorization (DNMF) models are interpretable via hierarchical learning but are linear and sensitive to topological noise. We propose GCNCDNMF, a framework that integrates graph convolutional networks (GCNs) with a constrained deep nonnegative matrix factorization (CDNMF) module. The CDNMF component uses a deep autoencoder-like structure with graph regularization to preserve community structures. The hierarchical embeddings from CDNMF are injected into the GCN propagation steps, which mitigates over-smoothing. In return, the GCN’s non-linear reconstructions refine the network topology and feed back to CDNMF, improving noise robustness. Experiments on five real-world benchmark datasets (Cora, Citeseer, Email, Cornell, and Texas) show that GCNCDNMF consistently outperforms state-of-the-art methods in accuracy, normalized mutual information, and adjusted Rand index. The code for this work is publicly available at: https://github.com/LiShunli0719/GCNCDNMF_main.