Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence

Norikazu Takahashi, Masato Seki

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

3 Citations (Scopus)

Abstract

Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.

Original languageEnglish
Title of host publication2016 24th European Signal Processing Conference, EUSIPCO 2016
PublisherEuropean Signal Processing Conference, EUSIPCO
Pages438-442
Number of pages5
Volume2016-November
ISBN (Electronic)9780992862657
DOIs
Publication statusPublished - Nov 28 2016
Event24th European Signal Processing Conference, EUSIPCO 2016 - Budapest, Hungary
Duration: Aug 28 2016Sep 2 2016

Other

Other24th European Signal Processing Conference, EUSIPCO 2016
CountryHungary
CityBudapest
Period8/28/169/2/16

Fingerprint

Constrained optimization
Factorization
Polynomials
Computational methods

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Takahashi, N., & Seki, M. (2016). Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. In 2016 24th European Signal Processing Conference, EUSIPCO 2016 (Vol. 2016-November, pp. 438-442). [7760286] European Signal Processing Conference, EUSIPCO. https://doi.org/10.1109/EUSIPCO.2016.7760286

Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. / Takahashi, Norikazu; Seki, Masato.

2016 24th European Signal Processing Conference, EUSIPCO 2016. Vol. 2016-November European Signal Processing Conference, EUSIPCO, 2016. p. 438-442 7760286.

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

Takahashi, N & Seki, M 2016, Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. in 2016 24th European Signal Processing Conference, EUSIPCO 2016. vol. 2016-November, 7760286, European Signal Processing Conference, EUSIPCO, pp. 438-442, 24th European Signal Processing Conference, EUSIPCO 2016, Budapest, Hungary, 8/28/16. https://doi.org/10.1109/EUSIPCO.2016.7760286
Takahashi N, Seki M. Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. In 2016 24th European Signal Processing Conference, EUSIPCO 2016. Vol. 2016-November. European Signal Processing Conference, EUSIPCO. 2016. p. 438-442. 7760286 https://doi.org/10.1109/EUSIPCO.2016.7760286
Takahashi, Norikazu ; Seki, Masato. / Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. 2016 24th European Signal Processing Conference, EUSIPCO 2016. Vol. 2016-November European Signal Processing Conference, EUSIPCO, 2016. pp. 438-442
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