A damped Newton algorithm for nonnegative matrix factorization based on alpha-divergence

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Abstract

A novel Newton-type algorithm for nonnegative matrix factorization based on α-divergence is proposed in this paper. The proposed algorithm is a cyclic coordinate descent algorithm that decreases the objective function value along one coordinate direction at a time by using a damped Newton method for monotone equations. It is proved that the proposed algorithm has the global convergence property in the sense of Zangwill. It is also shown experimentally that the proposed algorithm is fast, independent of the value of α while conventional algorithms become very slow for some values of α.

Original languageEnglish
Title of host publication2019 6th International Conference on Systems and Informatics, ICSAI 2019
EditorsWanqing Wu, Lipo Wang, Chunlei Ji, Niansheng Chen, Sun Qiang, Xiaoyong Song, Xin Wang
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages463-468
Number of pages6
ISBN (Electronic)9781728152561
DOIs
Publication statusPublished - Nov 2019
Event6th International Conference on Systems and Informatics, ICSAI 2019 - Shanghai, China
Duration: Nov 2 2019Nov 4 2019

Publication series

Name2019 6th International Conference on Systems and Informatics, ICSAI 2019

Conference

Conference6th International Conference on Systems and Informatics, ICSAI 2019
CountryChina
CityShanghai
Period11/2/1911/4/19

Keywords

  • Damped Newton method
  • Divergence
  • Global convergence
  • Nonnegative matrix factorization

ASJC Scopus subject areas

  • Health Informatics
  • Computer Vision and Pattern Recognition
  • Information Systems
  • Control and Systems Engineering
  • Mechanical Engineering
  • Control and Optimization

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  • Cite this

    Sano, T., Migita, T., & Takahashi, N. (2019). A damped Newton algorithm for nonnegative matrix factorization based on alpha-divergence. In W. Wu, L. Wang, C. Ji, N. Chen, S. Qiang, X. Song, & X. Wang (Eds.), 2019 6th International Conference on Systems and Informatics, ICSAI 2019 (pp. 463-468). [9010306] (2019 6th International Conference on Systems and Informatics, ICSAI 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICSAI48974.2019.9010306