Geometrical formulation of the nonnegative matrix factorization

Shotaro Akaho; Hideitsu Hino; Neneka Nara; Noboru Murata

doi:10.1007/978-3-030-04182-3_46

Geometrical formulation of the nonnegative matrix factorization

Shotaro Akaho, Hideitsu Hino, Neneka Nara, Noboru Murata

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

Nonnegative matrix factorization (NMF) has many applications as a tool for dimension reduction. In this paper, we reformulate the NMF from an information geometrical viewpoint. We show that a conventional optimization criterion is not geometrically natural, thus we propose to use more natural criterion. By this formulation, we can apply a geometrical algorithm based on the Pythagorean theorem. We also show the algorithm can improve the existing algorithm through numerical experiments.

本文言語	English
ホスト出版物のタイトル	Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings
編集者	Long Cheng, Seiichi Ozawa, Andrew Chi Sing Leung
出版社	Springer-Verlag
ページ	525-534
ページ数	10
ISBN（印刷版）	9783030041816
DOI	https://doi.org/10.1007/978-3-030-04182-3_46
出版ステータス	Published - 2018 1 1
イベント	25th International Conference on Neural Information Processing, ICONIP 2018 - Siem Reap, Cambodia 継続期間: 2018 12 13 → 2018 12 16

出版物シリーズ

名前	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
巻	11303 LNCS
ISSN（印刷版）	0302-9743
ISSN（電子版）	1611-3349

Other

Other	25th International Conference on Neural Information Processing, ICONIP 2018
Country	Cambodia
City	Siem Reap
Period	18/12/13 → 18/12/16

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

文献へのアクセス

10.1007/978-3-030-04182-3_46

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引用スタイル

Akaho, S., Hino, H., Nara, N., & Murata, N. (2018). Geometrical formulation of the nonnegative matrix factorization. In L. Cheng, S. Ozawa, & A. C. S. Leung (Eds.), Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings (pp. 525-534). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11303 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-04182-3_46

Geometrical formulation of the nonnegative matrix factorization. / Akaho, Shotaro; Hino, Hideitsu; Nara, Neneka; Murata, Noboru.

Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. ed. / Long Cheng; Seiichi Ozawa; Andrew Chi Sing Leung. Springer-Verlag, 2018. p. 525-534 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11303 LNCS).

研究成果: Conference contribution

Akaho, S, Hino, H, Nara, N & Murata, N 2018, Geometrical formulation of the nonnegative matrix factorization. in L Cheng, S Ozawa & ACS Leung (eds), Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11303 LNCS, Springer-Verlag, pp. 525-534, 25th International Conference on Neural Information Processing, ICONIP 2018, Siem Reap, Cambodia, 18/12/13. https://doi.org/10.1007/978-3-030-04182-3_46

Akaho S, Hino H, Nara N, Murata N. Geometrical formulation of the nonnegative matrix factorization. In Cheng L, Ozawa S, Leung ACS, editors, Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. Springer-Verlag. 2018. p. 525-534. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-04182-3_46

Akaho, Shotaro ; Hino, Hideitsu ; Nara, Neneka ; Murata, Noboru. / Geometrical formulation of the nonnegative matrix factorization. Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings. editor / Long Cheng ; Seiichi Ozawa ; Andrew Chi Sing Leung. Springer-Verlag, 2018. pp. 525-534 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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