Lévy NMF for Robust Nonnegative Source Separation

Paul Magron 1, 2 Roland Badeau 2 Antoine Liutkus 3
3 MULTISPEECH - Speech Modeling for Facilitating Oral-Based Communication
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Source separation, which consists in decomposing data into meaningful structured components, is an active research topic in music signal processing. In this paper, we introduce the Positive α-stable (PαS) distributions to model the latent sources, which are a sub- class of the stable distributions family. They notably permit us to model random variables that are both nonnegative and impulsive. Considering the Lévy distribution, the only PαS distribution whose density is tractable, we propose a mixture model called Lévy Non- negative Matrix Factorization (Lévy NMF). This model accounts for low-rank structures in nonnegative data that possibly has high variability or is corrupted by very adverse noise. The model parameters are estimated in a maximum-likelihood sense. We also derive an estimator of the sources, which extends the validity of the Wiener filtering to the PαS case. Experiments on synthetic data and realistic music signals show that Lévy NMF compares favorably with state-of-the art techniques in terms of robustness to impulsive noise and highlight its potential for decomposing nonnegative data.
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Paul Magron, Roland Badeau, Antoine Liutkus. Lévy NMF for Robust Nonnegative Source Separation. IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA 2017), IEEE, Oct 2017, New Paltz, NY, United States. ⟨hal-01548488⟩

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