Symmetry and Nonnegativity-Constrained Matrix Factorization for Community Detection
Zhigang Liu, Guangxiao Yuan, Xin Luo
Abstract
Dear Editor, This letter presents a novel symmetry and nonnegativity-constrained matrix factorization (SNCMF)-based community detection model on undirected networks such as a social network. Community is a fundamental characteristic of a network, making community detection a vital yet thorny issue in network representation. Owing to its high interpretability and scalability, a symmetric nonnegative matrix factorization (SNMF) model is frequently adopted to address this issue. However, it adopts a unique latent factor (LF) matrix for representing an undirected network's symmetry, which leads to a reduced latent space that impairs its representation learning ability. Motivated by this discovery, the proposed SNCMF model innovatively adopts the following three-fold ideas: 1) Leveraging multiple LF matrices to represent a network, thereby enhancing its representation learning ability; 2) Introducing a symmetry regularization term that implies the equality constraint between multiple LF matrices to illustrate the network's symmetry; and 3) Incorporating graph regularization into the model to preserve the network's intrinsic geometry. Experimental results on several real-world networks indicate that the proposed SNCMF-based community detector outperforms the benchmark and state-of-the-art models in achieving highly-accurate community detection results.