Community detection via graph regularized symmetric nonnegative matrix tri-factorization

Abstract Identifying meaningful communities in complex networks is essential for uncovering functional structures in social, biological, and technological systems. Despite the success of Nonnegative Matrix Factorization (NMF) methods, most existing approaches fail to simultaneously preserve local structural patterns, enforce clear community separation, and effectively handle the sparsity of real-world graphs. To address these challenges, we propose SPD-SNMTF , a Structural Proximity and Diagonalized Symmetric Nonnegative Matrix Tri-Factorization framework that integrates three key components: (1) a hybrid similarity matrix combining explicit links and latent neighborhood affinities; (2) diagonal dominance constraints to enhance inter-community separation; and (3) graph Laplacian regularization to preserve topological smoothness. This unified approach jointly reconstructs the adjacency matrix while enforcing geometric and sparsity-aware constraints, resulting in more interpretable community detection with stable performance across a wide range of parameter settings. Experiments on eleven real-world datasets demonstrate that SPD-SNMTF consistently outperforms twelve state-of-the-art methods in terms of NMI, ACC, and ARI. Implementation details are available at https://github.com/sohrabi94/SPD-SNMTF .