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

Ryota Hibi; Norikazu Takahashi

doi:10.1007/978-3-642-24958-7_76

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 proceeding › Conference contribution

8 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 language	English
Title of host publication	Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings
Pages	655-662
Number of pages	8
Edition	PART 2
DOIs	https://doi.org/10.1007/978-3-642-24958-7_76
Publication status	Published - Nov 28 2011
Externally published	Yes
Event	18th International Conference on Neural Information Processing, ICONIP 2011 - Shanghai, China Duration: Nov 13 2011 → Nov 17 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 2
Volume	7063 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	18th International Conference on Neural Information Processing, ICONIP 2011
Country/Territory	China
City	Shanghai
Period	11/13/11 → 11/17/11

Keywords

Euclidean distance
global convergence
multiplicative update
nonnegative matrix factorization

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-642-24958-7_76

Cite this

Hibi, R., & Takahashi, N. (2011). A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. In Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings (PART 2 ed., 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.
Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings. 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 proceeding › Conference contribution

Hibi, R & Takahashi, N 2011, A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence. in Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings. PART 2 edn, 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 Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings. PART 2 ed. 2011. p. 655-662. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 2). doi: 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. Neural Information Processing - 18th International Conference, ICONIP 2011, Proceedings. 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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A modified multiplicative update algorithm for euclidean distance-based nonnegative matrix factorization and its global convergence

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Keywords

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