A Stochastic Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization


Songtao Lu, Mingyi Hong, Zhengdao Wang ;
Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:812-821, 2017.


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.

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