Nonnegative Residual Matrix Factorization for Community Detection

Abstract

Community detection is one of the most important and challenging problems in graph mining and social network analysis. Nonnegative Matrix Factorization (NMF) based methods have been proved to be effective in the task of community detection. However, real-world networks could be noisy and existing NMF based community detection methods are sensitive to the outliers and noise due to the utilization of the squared loss function to measure the quality of graph regularization and network reconstruction. In this paper, we propose a framework based on the nonnegative residual matrix factorization (NRMF) to overcome this limitation. In this method, a residual matrix, represented by the matrix reconstruction error, is explicitly introduced to capture the impact of outliers and noise. The residual matrix should be sparse intuitively so some sparse regularization can be used to model the sparsity. Specifically, three different types of sparse regularization, i.e., $L_0$, $L_{1}$ and $L_{2,1}$, have been studied. Multiplicative update rules and different thresholding operators are used to learn these lower-rank matrices. Extensive experiments on benchmark networks with and without known communities demonstrate that our framework is more robust so that it outperforms state-of-the-art NMF based approaches in community detection task.