A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality

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 guar...

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Bibliographic Details
Published inIEEE transactions on signal processing Vol. 65; no. 12; pp. 3120 - 3135
Main Authors Lu, Songtao, Hong, Mingyi, Wang, Zhengdao
Format Journal Article
LanguageEnglish
Published IEEE 15.06.2017
Subjects
Algorithm design and analysis
clustering
Clustering algorithms
Convergence
global and local optimality
Karush-Kuhn-Tucker points
Linear programming
Matrix decomposition
Signal processing algorithms
Symmetric matrices
Symmetric nonnegative matrix factorization
variable splitting
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Summary: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 that guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real datasets suggest that the proposed algorithm converges quickly to a local minimum solution.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2679687