A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence

Satoshi Nakatsu, Norikazu Takahashi

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

Abstract

We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.

Original languageEnglish
Title of host publicationNeural Information Processing - 24th International Conference, ICONIP 2017, Proceedings
PublisherSpringer Verlag
Pages335-344
Number of pages10
Volume10634 LNCS
ISBN (Print)9783319700861
DOIs
Publication statusPublished - Jan 1 2017
Event24th International Conference on Neural Information Processing, ICONIP 2017 - Guangzhou, China
Duration: Nov 14 2017Nov 18 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10634 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other24th International Conference on Neural Information Processing, ICONIP 2017
CountryChina
CityGuangzhou
Period11/14/1711/18/17

Fingerprint

Non-negative Matrix Factorization
Factorization
Divergence
Subsequence
Coordinate Descent
Stationary point
Global Convergence
Newton Methods
Convergence Properties
Iterative Algorithm
Multiplicative
Newton-Raphson method
Update
Numerical Experiment
Optimization Problem
Experiments

Keywords

  • Alpha-divergence
  • Global convergence
  • Newton method
  • Nonnegative matrix factorization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Nakatsu, S., & Takahashi, N. (2017). A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. In Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings (Vol. 10634 LNCS, pp. 335-344). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10634 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-70087-8_36

A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. / Nakatsu, Satoshi; Takahashi, Norikazu.

Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings. Vol. 10634 LNCS Springer Verlag, 2017. p. 335-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10634 LNCS).

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

Nakatsu, S & Takahashi, N 2017, A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. in Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings. vol. 10634 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10634 LNCS, Springer Verlag, pp. 335-344, 24th International Conference on Neural Information Processing, ICONIP 2017, Guangzhou, China, 11/14/17. https://doi.org/10.1007/978-3-319-70087-8_36
Nakatsu S, Takahashi N. A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. In Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings. Vol. 10634 LNCS. Springer Verlag. 2017. p. 335-344. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-70087-8_36
Nakatsu, Satoshi ; Takahashi, Norikazu. / A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings. Vol. 10634 LNCS Springer Verlag, 2017. pp. 335-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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