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 language | English (US) |
|---|---|
| Title of host publication | 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 8202-8206 |
| Number of pages | 5 |
| ISBN (Electronic) | 9781479981311 |
| DOIs | |
| State | Published - May 2019 |
| Event | 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom Duration: May 12 2019 → May 17 2019 |
Publication series
| Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
|---|---|
| Volume | 2019-May |
| ISSN (Print) | 1520-6149 |
Conference
| Conference | 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 |
|---|---|
| Country | United Kingdom |
| City | Brighton |
| Period | 5/12/19 → 5/17/19 |
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Keywords
- Nonnegative matrix factorization (NMF)
- majorization-minimization (MM)
ASJC Scopus subject areas
- Software
- Signal Processing
- Electrical and Electronic Engineering
Cite this
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 proceeding › Conference contribution
}
TY - GEN
T1 - Majorization-minimization Algorithms for Convolutive NMF with the Beta-divergence
AU - Fagot, Dylan
AU - Wendt, Herwig
AU - Févotte, Cédric
AU - Smaragdis, Paris
PY - 2019/5
Y1 - 2019/5
N2 - 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.
AB - 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.
KW - Nonnegative matrix factorization (NMF)
KW - majorization-minimization (MM)
UR - http://www.scopus.com/inward/record.url?scp=85069442040&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85069442040&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2019.8683837
DO - 10.1109/ICASSP.2019.8683837
M3 - Conference contribution
AN - SCOPUS:85069442040
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 8202
EP - 8206
BT - 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
ER -