Robust Low-Rank Tensor Constrained Orthogonal Symmetric Non-Negative Matrix Factorization for Multi-Layer Networks Community Detection

In multi-layer network community detection, the goal is to group nodes into distinct clusters based on their connection strengths. Currently, many existing methods do not fully leverage the relationships between layers, and observed multi-layer networks often contain noise that can significantly impact the accuracy of community detection. To address these challenges, a robust low-rank tensor constrained orthogonal symmetric non-negative matrix factorization method for multi-layer network community detection (RTOSNMF) is introduced. Specifically, noise is separated from raw adjacency matrices using linear separation, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2,1}$</tex-math></inline-formula> norm constraint is applied to achieve denoising. Clean adjacency matrices are then used to perform orthogonal symmetric non-negative matrix factorization, extracting latent representations of the multi-layer networks. Moreover, the nuclear norm is utilized to preserve the low-rank property of the adjacency tensor, aiding in the discovery of higher-order inter-layer relationships. An algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed to solve the RTOSNMF model. Extensive experiments conducted on eight datasets demonstrate superior performance of the proposed model compared with fifteen state-of-the-art methods.