A nonconvex splitting method for symmetric nonnegative matrix factorization: Convergence analysis and optimality

Songtao Lu, Mingyi Hong, Zhengdao Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Symmetric non-negative 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. Different from the existing works, we prove that the algorithm converges to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem with a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in a distributed manner. Further, we provide sufficient conditions that 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 yields high quality of the solutions and converges quickly to the set of local minimum solutions compared with other algorithms.

Original languageEnglish (US)
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2572-2576
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - Jun 16 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: Mar 5 2017Mar 9 2017

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
CountryUnited States
CityNew Orleans
Period3/5/173/9/17

Bibliographical note

Publisher Copyright:
© 2017 IEEE.

Keywords

  • Karush-Kuhn-Tucker points
  • Symmetric Nonnegative Matrix Factorization
  • clustering
  • global and local optimality
  • variable splitting

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