A stochastic nonconvex splitting method for symmetric nonnegative matrix factorization

Symmetric nonnegative matrix factorization (SymNMF) plays an important role in applications of many data analytics problems such as community detection, document clustering and image segmentation. In this paper, we consider a stochastic SymNMF problem in which the observation matrix is generated in a random and sequential manner. We propose a stochastic nonconvex splitting method, which not only guarantees convergence to the set of stationary points of the problem (in the mean-square sense), but further achieves a sublinear convergence rate. Numerical results show that for clustering problems over both synthetic and real world datasets, the proposed algorithm converges quickly to the set of stationary points.