A Multi-Constrained Matrix Factorization Approach for Community Detection Relying on Alternating-Direction-Method of Multipliers

Dear editor, This letter presents a novel multi-constrained matrix factorization (MMF) approach via the alternating-direction-method of multipliers (ADMM) for building a highly-accurate community detector on an undirected network. In the area of network science, aiming to identify cohesive structure of a network, community detection is considered as a clustering task for network nodes, and has attracted much attention since it reveals how a network is organized and developed. In general, non-negative matrix factorization (NMF) is an effective approach to tackling this problem owing to its good interpretability for cluster structure. However, it does not capture the inherent symmetry of an undirected network. Symmetric and non-negative matrix factorization (SNMF) adopts a single feature matrix to learn a target undirected network's low-rank approximation, thus preserving the network's symmetry. Nonetheless, its representation learning ability would be inevitably limited by the reduced feature space. Inspired by the above findings, MMF innovatively adopts four-fold ideas: 1) Using multiple feature matrices to expand the representation space and its flexibility; 2) Imposing relaxed symmetry constraints to capture the network's inherent symmetry; 3) Applying graph regularization to preserve the network's geometric structure and community features; and 4) Separating constraints from decision variables and using ADMM to derive an efficient learning algorithm. Experiments on four social networks show that MMF outperforms the baseline and state-of-the-art models in achieving high-precision community detection.