Title: A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality,
Abstract: Symmetric nonnegative matrix factorization (SymNMF) has important
applications in data analytics problems such as document clustering, community
detection and image segmentation. In this paper, we propose a novel nonconvex
variable splitting method for solving SymNMF. The proposed algorithm is
guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the
nonconvex SymNMF problem. Furthermore, it achieves a global sublinear
convergence rate. We also show that the algorithm can be efficiently
implemented in parallel. Further, sufficient conditions are provided which
guarantee the global and local optimality of the obtained solutions. Extensive
numerical results performed on both synthetic and real data sets suggest that
the proposed algorithm converges quickly to a local minimum solution.