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Community is a fundamental and critical characteristic of a Large-scaleUndirected Network (LUN) like a social network, making community detection avital yet thorny issue in LUN representation learning. Owing to its goodscalability and interpretability, a Symmetric and Nonnegative MatrixFactorization (SNMF) model is commonly used to tackle this issue. However, itadopts a unique Latent Factor (LF) matrix for precisely representing an LUN'ssymmetry, which leads to a reduced LF space that impairs its representationallearning ability. Motivated by this discovery, this study proposes a Symmetryand Graph-regularized Nonnegative Matrix Factorization (SGNMF) method thatadopts three-fold ideas: a) leveraging multiple LF matrices to represent anLUN, thereby enhancing its representation learning ability; b) introducing asymmetry regularization term that implies the equality constraint between itsmultiple LF matrices, thereby illustrating an LUN's symmetry; and c)incorporating graph regularization into its learning objective, therebyillustrating an LUN's intrinsic geometry. A theoretical proof is provided toensure SGNMF's convergence on an LUN. Extensive experiment results on ten LUNsfrom real applications demonstrate that our proposed SGNMF-based communitydetector significantly outperforms several baseline and state-of-the-art modelsin achieving highly-accurate results for community detection.

A Symmetry and Graph Regularized Nonnegative Matrix Factorization Model for Community Detection