Boundedness of modified multiplicative updates for nonnegative matrix factorization

Jiro Katayama, Norikazu Takahashi, Jun'Ichi Takeuchi

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

3 Citations (Scopus)

Abstract

There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.

Original languageEnglish
Title of host publication2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
Pages252-255
Number of pages4
DOIs
Publication statusPublished - 2013
Event2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013 - Saint Martin, France
Duration: Dec 15 2013Dec 18 2013

Other

Other2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
CountryFrance
CitySaint Martin
Period12/15/1312/18/13

Fingerprint

Factorization

ASJC Scopus subject areas

  • Computer Science Applications

Cite this

Katayama, J., Takahashi, N., & Takeuchi, JI. (2013). Boundedness of modified multiplicative updates for nonnegative matrix factorization. In 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013 (pp. 252-255). [6714055] https://doi.org/10.1109/CAMSAP.2013.6714055

Boundedness of modified multiplicative updates for nonnegative matrix factorization. / Katayama, Jiro; Takahashi, Norikazu; Takeuchi, Jun'Ichi.

2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013. 2013. p. 252-255 6714055.

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

Katayama, J, Takahashi, N & Takeuchi, JI 2013, Boundedness of modified multiplicative updates for nonnegative matrix factorization. in 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013., 6714055, pp. 252-255, 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, Saint Martin, France, 12/15/13. https://doi.org/10.1109/CAMSAP.2013.6714055
Katayama J, Takahashi N, Takeuchi JI. Boundedness of modified multiplicative updates for nonnegative matrix factorization. In 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013. 2013. p. 252-255. 6714055 https://doi.org/10.1109/CAMSAP.2013.6714055
Katayama, Jiro ; Takahashi, Norikazu ; Takeuchi, Jun'Ichi. / Boundedness of modified multiplicative updates for nonnegative matrix factorization. 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013. 2013. pp. 252-255
@inproceedings{ca54eb3973e74556aec21a57964a200b,
title = "Boundedness of modified multiplicative updates for nonnegative matrix factorization",
abstract = "There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.",
author = "Jiro Katayama and Norikazu Takahashi and Jun'Ichi Takeuchi",
year = "2013",
doi = "10.1109/CAMSAP.2013.6714055",
language = "English",
isbn = "9781467331463",
pages = "252--255",
booktitle = "2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013",

}

TY - GEN

T1 - Boundedness of modified multiplicative updates for nonnegative matrix factorization

AU - Katayama, Jiro

AU - Takahashi, Norikazu

AU - Takeuchi, Jun'Ichi

PY - 2013

Y1 - 2013

N2 - There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.

AB - There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.

UR - http://www.scopus.com/inward/record.url?scp=84894118092&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894118092&partnerID=8YFLogxK

U2 - 10.1109/CAMSAP.2013.6714055

DO - 10.1109/CAMSAP.2013.6714055

M3 - Conference contribution

AN - SCOPUS:84894118092

SN - 9781467331463

SP - 252

EP - 255

BT - 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013

ER -