Global convergence of a modified HALS algorithm for nonnegative matrix factorization

Takumi Kimura, Norikazu Takahashi

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

4 Citations (Scopus)

Abstract

Hierarchical alternating least squares (HALS) algorithms are efficient computational methods for nonnegative matrix factorization (NMF). Given an initial solution, HALS algorithms update the solution block by block iteratively so that the error decreases monotonically. However, update rules in HALS algorithms are not well-defined. In addition, due to this problem, the convergence of the sequence of solutions to a stationary point cannot be proved theoretically. In this paper, we consider the HALS algorithm for the Frobenius norm-based NMF, and prove that a modified version has the global convergence property in the sense of Zangwill.

Original languageEnglish
Title of host publication2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages21-24
Number of pages4
ISBN (Print)9781479919635
DOIs
Publication statusPublished - Jan 14 2016
Event6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 - Cancun, Mexico
Duration: Dec 13 2015Dec 16 2015

Other

Other6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
CountryMexico
CityCancun
Period12/13/1512/16/15

Fingerprint

Alternating Least Squares
Non-negative Matrix Factorization
Least Square Algorithm
Factorization
Global Convergence
Update
Frobenius norm
Stationary point
Computational methods
Computational Methods
Convergence Properties
Well-defined
Decrease

ASJC Scopus subject areas

  • Signal Processing
  • Computational Mathematics

Cite this

Kimura, T., & Takahashi, N. (2016). Global convergence of a modified HALS algorithm for nonnegative matrix factorization. In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 (pp. 21-24). [7383726] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAMSAP.2015.7383726

Global convergence of a modified HALS algorithm for nonnegative matrix factorization. / Kimura, Takumi; Takahashi, Norikazu.

2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc., 2016. p. 21-24 7383726.

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

Kimura, T & Takahashi, N 2016, Global convergence of a modified HALS algorithm for nonnegative matrix factorization. in 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015., 7383726, Institute of Electrical and Electronics Engineers Inc., pp. 21-24, 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015, Cancun, Mexico, 12/13/15. https://doi.org/10.1109/CAMSAP.2015.7383726
Kimura T, Takahashi N. Global convergence of a modified HALS algorithm for nonnegative matrix factorization. In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc. 2016. p. 21-24. 7383726 https://doi.org/10.1109/CAMSAP.2015.7383726
Kimura, Takumi ; Takahashi, Norikazu. / Global convergence of a modified HALS algorithm for nonnegative matrix factorization. 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 21-24
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