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Majorization-minimization algorithms for convolutive NMF with the beta-divergence

Fagot, Dylan and Wendt, Herwig and Févotte, Cédric and Smaragdis, Paris Majorization-minimization algorithms for convolutive NMF with the beta-divergence. (2019) In: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019), 12 May 2019 - 17 May 2019 (Brighton, United Kingdom).

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Official URL: https://doi.org/10.1109/ICASSP.2019.8683837


Nonnegative matrix factorization (NMF) has become a method ofchoice for spectrogram decomposition. However, its inability to cap-ture dependencies across columns of the input motivated the intro-duction of a variant, convolutive NMF. While algorithms for solv-ing the convolutive NMF problem were previously proposed, theyrely on the use of a heuristic that does not insure the convergenceof the algorithm (in particular in terms of objective function values).The goal of this work is to propose rigorous update rules, based ona majorization-minimization (MM) approach, for convolutive NMFwith theß-divergence (a standard family of measures of fit). Specif-ically, we derive and study two variants of a convolutive NMF al-gorithm that are guaranteed to decrease the objective function valueat each iteration. The complexity of the algorithms is studied, andthe performance in terms of execution time and objective functionare evaluated and compared in several numerical experiments usingreal-world audio data. Experiments show that the proposed MM al-gorithms consistently provide lower values of the objective functionthan the heuristic, at similar computational cost.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of ICASSP 2019 Electronic ISBN: 978-1-4799-8131-1 The original PDF of the article can be found at: https://ieeexplore.ieee.org/document/8683837 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-02378395
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > University of Illinois at Urbana-Champaign - UIUC (USA)
Laboratory name:
ERC : European Research Council (Europe) - European Union’s Horizon 2020 research and innovation program (Europe) - NSF : National Science Foundation (US)
Deposited On:19 Nov 2019 14:35

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