A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence

Ryota Hibi, Norikazu Takahashi

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

7 Citations (Scopus)

Abstract

Nonnegative matrix factorization (NMF) is to approximate a given large nonnegative matrix by the product of two small nonnegative matrices. Although the multiplicative update algorithm is widely used as an efficient computation method for NMF, it has a serious drawback that the update formulas are not well-defined because they are expressed in the form of a fraction. Furthermore, due to this drawback, the global convergence of the algorithm has not been guaranteed. In this paper, we consider NMF in which the approximation error is measured by the Euclidean distance between two matrices. We propose a modified multiplicative update algorithm in order to overcome the drawback of the original version and prove its global convergence.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages655-662
Number of pages8
Volume7063 LNCS
EditionPART 2
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event18th International Conference on Neural Information Processing, ICONIP 2011 - Shanghai, China
Duration: Nov 13 2011Nov 17 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume7063 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other18th International Conference on Neural Information Processing, ICONIP 2011
CountryChina
CityShanghai
Period11/13/1111/17/11

Fingerprint

Non-negative Matrix Factorization
Euclidean Distance
Factorization
Global Convergence
Multiplicative
Update
Nonnegative Matrices
Approximation Error
Well-defined

Keywords

  • Euclidean distance
  • global convergence
  • multiplicative update
  • nonnegative matrix factorization

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Hibi, R., & Takahashi, N. (2011). A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (PART 2 ed., Vol. 7063 LNCS, pp. 655-662). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7063 LNCS, No. PART 2). https://doi.org/10.1007/978-3-642-24958-7_76

A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. / Hibi, Ryota; Takahashi, Norikazu.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7063 LNCS PART 2. ed. 2011. p. 655-662 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7063 LNCS, No. PART 2).

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

Hibi, R & Takahashi, N 2011, A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 edn, vol. 7063 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 2, vol. 7063 LNCS, pp. 655-662, 18th International Conference on Neural Information Processing, ICONIP 2011, Shanghai, China, 11/13/11. https://doi.org/10.1007/978-3-642-24958-7_76
Hibi R, Takahashi N. A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). PART 2 ed. Vol. 7063 LNCS. 2011. p. 655-662. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). https://doi.org/10.1007/978-3-642-24958-7_76
Hibi, Ryota ; Takahashi, Norikazu. / A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7063 LNCS PART 2. ed. 2011. pp. 655-662 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2).
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