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

Abstract : 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.
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Submitted on : Monday, November 25, 2019 - 10:56:10 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:34 AM
Long-term archiving on: : Wednesday, February 26, 2020 - 2:10:43 PM

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  • HAL Id : hal-02361457, version 2
  • OATAO : 24968

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Dylan Fagot, Herwig Wendt, Cédric Févotte, Paris Smaragdis. Majorization-minimization algorithms for convolutive NMF with the beta-divergence. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2019), May 2019, Brighton, United Kingdom. pp.8202-8206. ⟨hal-02361457v2⟩

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