Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence

Dylan Fagot, Herwig Wendt, Cédric Févotte, Paris Smaragdis

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

Abstract

Nonnegative matrix factorization (NMF) has become a method of choice for spectrogram decomposition. However, its inability to capture dependencies across columns of the input motivated the introduction of a variant, convolutive NMF. While algorithms for solving the convolutive NMF problem were previously proposed, they rely on the use of a heuristic that does not insure the convergence of the algorithm (in particular in terms of objective function values). The goal of this work is to propose rigorous update rules, based on a majorization-minimization (MM) approach, for convolutive NMF with the β-divergence (a standard family of measures of fit). Specifically, we derive and study two variants of a convolutive NMF algorithm that are guaranteed to decrease the objective function value at each iteration. The complexity of the algorithms is studied, and the performance in terms of execution time and objective function are evaluated and compared in several numerical experiments using real-world audio data. Experiments show that the proposed MM algorithms consistently provide lower values of the objective function than the heuristic, at similar computational cost.

Original languageEnglish (US)
Title of host publication2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages8202-8206
Number of pages5
ISBN (Electronic)9781479981311
DOIs
StatePublished - May 2019
Event44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom
Duration: May 12 2019May 17 2019

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2019-May
ISSN (Print)1520-6149

Conference

Conference44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019
CountryUnited Kingdom
CityBrighton
Period5/12/195/17/19

Fingerprint

Factorization
Experiments
Decomposition
Costs

Keywords

  • Nonnegative matrix factorization (NMF)
  • majorization-minimization (MM)

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Fagot, D., Wendt, H., Févotte, C., & Smaragdis, P. (2019). Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings (pp. 8202-8206). [8683837] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2019.8683837

Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence. / Fagot, Dylan; Wendt, Herwig; Févotte, Cédric; Smaragdis, Paris.

2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 8202-8206 8683837 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings; Vol. 2019-May).

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

Fagot, D, Wendt, H, Févotte, C & Smaragdis, P 2019, Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence. in 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings., 8683837, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, vol. 2019-May, Institute of Electrical and Electronics Engineers Inc., pp. 8202-8206, 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019, Brighton, United Kingdom, 5/12/19. https://doi.org/10.1109/ICASSP.2019.8683837
Fagot D, Wendt H, Févotte C, Smaragdis P. Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence. In 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 8202-8206. 8683837. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2019.8683837
Fagot, Dylan ; Wendt, Herwig ; Févotte, Cédric ; Smaragdis, Paris. / Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence. 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 8202-8206 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).
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