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

Satoshi Nakatsu; Norikazu Takahashi

doi:10.1007/978-3-319-70087-8_36

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

Satoshi Nakatsu, Norikazu Takahashi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

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 language	English
Title of host publication	Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings
Publisher	Springer Verlag
Pages	335-344
Number of pages	10
Volume	10634 LNCS
ISBN (Print)	9783319700861
DOIs	https://doi.org/10.1007/978-3-319-70087-8_36
Publication status	Published - Jan 1 2017
Event	24th International Conference on Neural Information Processing, ICONIP 2017 - Guangzhou, China Duration: Nov 14 2017 → Nov 18 2017

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	10634 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	24th International Conference on Neural Information Processing, ICONIP 2017
Country	China
City	Guangzhou
Period	11/14/17 → 11/18/17

Keywords

Alpha-divergence
Global convergence
Newton method
Nonnegative matrix factorization

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-319-70087-8_36

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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 proceeding › Conference 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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