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

^*Corresponding author for this work

School of Advanced Science and Engineering

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

2 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings
Editors	Long Cheng, Seiichi Ozawa, Andrew Chi Sing Leung
Publisher	Springer Verlag
Pages	525-534
Number of pages	10
ISBN (Print)	9783030041816
DOIs	https://doi.org/10.1007/978-3-030-04182-3_46
Publication status	Published - 2018
Event	25th International Conference on Neural Information Processing, ICONIP 2018 - Siem Reap, Cambodia Duration: 2018 Dec 13 → 2018 Dec 16

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11303 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

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

Keywords

Dimension reduction
Information geometry
Topic model

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

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

Cite this

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 et al.
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).

Research output: Chapter in Book/Report/Conference proceeding › 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)). doi: 10.1007/978-3-030-04182-3_46

Akaho, Shotaro ; Hino, Hideitsu ; Nara, Neneka et al. / 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)).

@inproceedings{f714ed84c1874c3987911eb3dc0f7c0a,

title = "Geometrical formulation of the nonnegative matrix factorization",

abstract = "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.",

keywords = "Dimension reduction, Information geometry, Topic model",

author = "Shotaro Akaho and Hideitsu Hino and Neneka Nara and Noboru Murata",

note = "Funding Information: Supported by JSPS KAKENHI Grant Number 16K16108, 17H01793.; 25th International Conference on Neural Information Processing, ICONIP 2018 ; Conference date: 13-12-2018 Through 16-12-2018",

year = "2018",

doi = "10.1007/978-3-030-04182-3_46",

language = "English",

isbn = "9783030041816",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "525--534",

editor = "Long Cheng and Seiichi Ozawa and Leung, {Andrew Chi Sing}",

booktitle = "Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings",

}

TY - GEN

T1 - Geometrical formulation of the nonnegative matrix factorization

AU - Akaho, Shotaro

AU - Hino, Hideitsu

AU - Nara, Neneka

AU - Murata, Noboru

N1 - Funding Information: Supported by JSPS KAKENHI Grant Number 16K16108, 17H01793.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Dimension reduction

KW - Information geometry

KW - Topic model

UR - http://www.scopus.com/inward/record.url?scp=85059002284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059002284&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04182-3_46

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

M3 - Conference contribution

AN - SCOPUS:85059002284

SN - 9783030041816

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 525

EP - 534

BT - Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings

A2 - Cheng, Long

A2 - Ozawa, Seiichi

A2 - Leung, Andrew Chi Sing

PB - Springer Verlag

T2 - 25th International Conference on Neural Information Processing, ICONIP 2018

Y2 - 13 December 2018 through 16 December 2018

ER -

Geometrical formulation of the nonnegative matrix factorization

Abstract

Publication series

Other

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this