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.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v54-lu17a, title = {{A Stochastic Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization}}, author = {Lu, Songtao and Hong, Mingyi and Wang, Zhengdao}, booktitle = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics}, pages = {812--821}, year = {2017}, editor = {Singh, Aarti and Zhu, Jerry}, volume = {54}, series = {Proceedings of Machine Learning Research}, month = {20--22 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v54/lu17a/lu17a.pdf}, url = {https://proceedings.mlr.press/v54/lu17a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T A Stochastic Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization %A Songtao Lu %A Mingyi Hong %A Zhengdao Wang %B Proceedings of the 20th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2017 %E Aarti Singh %E Jerry Zhu %F pmlr-v54-lu17a %I PMLR %P 812--821 %U https://proceedings.mlr.press/v54/lu17a.html %V 54 %X 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.
APA
Lu, S., Hong, M. & Wang, Z.. (2017). A Stochastic Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 54:812-821 Available from https://proceedings.mlr.press/v54/lu17a.html.

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