WSNMF: Weighted Symmetric Nonnegative Matrix Factorization for attributed graph clustering

In recent times, Symmetric Nonnegative Matrix Factorization (SNMF), a derivative of Nonnegative Matrix Factorization (NMF), has surfaced as a promising technique for graph clustering. Nevertheless, when applied to attributed graph clustering, it confronts notable challenges. These include the disregard for attributed information, the oversight of geometric data point structures, and the inability to discriminate irrelevant features and data outliers. In response, we introduce an innovative extension of SNMF termed Weighted Symmetric Nonnegative Matrix Factorization (WSNMF). This method introduces node attribute similarity to compute a weight matrix, effectively bridging the gap for attributed graph clustering. Our approach incorporates graph regularization and sparsity constraints to uphold the geometric structure of data points and discern irrelevant features and data outliers. Additionally, we present an updating rule to address optimization complexities and validate algorithmic convergence. Rigorous experimentation on real-world and synthetic networks, employing well-established metrics including F-measure, RI, Modularity, Density, and entropy, substantiates the performance enhancement offered by WSNMF.