Graph Regularized Symmetric Non-Negative Matrix Factorization for Graph Clustering

Abstract

Symmetric non-negative matrix factorization (Sym-NMF) decomposes a high-dimensional symmetric non-negative matrix into a low-dimensional non-negative matrix and has been successfully used in graph clustering. In this paper, we propose a graph regularized symmetric non-negative matrix factorization (GrSymNMF) to enhance its performance in graph clustering. Particularly, GrSymNMF encodes the geometric structure so that the nearby points remain close to each other in the clustering domain. We optimize GrSymNMF by using a greedy coordinate descent algorithm and provide a distributed computing strategy to deploy GrSymNMF to large-scale datasets because it requires few communication overheads among computing nodes. The experiments on complex graph datasets and text corpus datasets verify the performance of GrSymNMF and efficiency, scalability and effectiveness of the distributed strategy of GrSymNMF.