Nonnegative matrix factorization with the Itakura-Saito divergence: with application to music analysis.
Identifieur interne : 001677 ( Main/Exploration ); précédent : 001676; suivant : 001678Nonnegative matrix factorization with the Itakura-Saito divergence: with application to music analysis.
Auteurs : Cédric Févotte [France] ; Nancy Bertin ; Jean-Louis DurrieuSource :
- Neural computation [ 0899-7667 ] ; 2009.
Descripteurs français
- KwdFr :
- Algorithmes (MeSH), Chaines de Markov (MeSH), Facteurs temps (MeSH), Humains (MeSH), Modèles statistiques (MeSH), Musique (MeSH), Mémorisation et recherche des informations (MeSH), Perception de la hauteur tonale (physiologie), Reconnaissance automatique des formes (MeSH), Spectrographie sonore (méthodes), Stimulation acoustique (MeSH).
- MESH :
English descriptors
- KwdEn :
- MESH :
Abstract
This letter presents theoretical, algorithmic, and experimental results about nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We describe how IS-NMF is underlaid by a well-defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters. This setting can accommodate regularization constraints on the factors through Bayesian priors. In particular, inverse-gamma and gamma Markov chain priors are considered in this work. Estimation can be carried out using a space-alternating generalized expectation-maximization (SAGE) algorithm; this leads to a novel type of NMF algorithm, whose convergence to a stationary point of the IS cost function is guaranteed. We also discuss the links between the IS divergence and other cost functions used in NMF, in particular, the Euclidean distance and the generalized Kullback-Leibler (KL) divergence. As such, we describe how IS-NMF can also be performed using a gradient multiplicative algorithm (a standard algorithm structure in NMF) whose convergence is observed in practice, though not proven. Finally, we report a furnished experimental comparative study of Euclidean-NMF, KL-NMF, and IS-NMF algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions, with various initializations and model orders. Then we show how IS-NMF can successfully be employed for denoising and upmix (mono to stereo conversion) of an original piece of early jazz music. These experiments indicate that IS-NMF correctly captures the semantics of audio and is better suited to the representation of music signals than NMF with the usual Euclidean and KL costs.
DOI: 10.1162/neco.2008.04-08-771
PubMed: 18785855
Affiliations:
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Le document en format XML
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theoretical, algorithmic, and experimental results about nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We describe how IS-NMF is underlaid by a well-defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters. This setting can accommodate regularization constraints on the factors through Bayesian priors. In particular, inverse-gamma and gamma Markov chain priors are considered in this work. Estimation can be carried out using a space-alternating generalized expectation-maximization (SAGE) algorithm; this leads to a novel type of NMF algorithm, whose convergence to a stationary point of the IS cost function is guaranteed. We also discuss the links between the IS divergence and other cost functions used in NMF, in particular, the Euclidean distance and the generalized Kullback-Leibler (KL) divergence. As such, we describe how IS-NMF can also be performed using a gradient multiplicative algorithm (a standard algorithm structure in NMF) whose convergence is observed in practice, though not proven. Finally, we report a furnished experimental comparative study of Euclidean-NMF, KL-NMF, and IS-NMF algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions, with various initializations and model orders. Then we show how IS-NMF can successfully be employed for denoising and upmix (mono to stereo conversion) of an original piece of early jazz music. These experiments indicate that IS-NMF correctly captures the semantics of audio and is better suited to the representation of music signals than NMF with the usual Euclidean and KL costs.</div></front></TEI><pubmed><MedlineCitation Status="MEDLINE" Owner="NLM"><PMID Version="1">18785855</PMID><DateCompleted><Year>2009</Year><Month>03</Month><Day>31</Day></DateCompleted><DateRevised><Year>2009</Year><Month>02</Month><Day>27</Day></DateRevised><Article PubModel="Print"><Journal><ISSN IssnType="Print">0899-7667</ISSN><JournalIssue CitedMedium="Print"><Volume>21</Volume><Issue>3</Issue><PubDate><Year>2009</Year><Month>Mar</Month></PubDate></JournalIssue><Title>Neural computation</Title><ISOAbbreviation>Neural Comput</ISOAbbreviation></Journal><ArticleTitle>Nonnegative matrix factorization with the Itakura-Saito divergence: with application to music analysis.</ArticleTitle><Pagination><MedlinePgn>793-830</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1162/neco.2008.04-08-771</ELocationID><Abstract><AbstractText>This letter presents theoretical, algorithmic, and experimental results about nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We describe how IS-NMF is underlaid by a well-defined statistical model of superimposed gaussian components and is equivalent to maximum likelihood estimation of variance parameters. This setting can accommodate regularization constraints on the factors through Bayesian priors. In particular, inverse-gamma and gamma Markov chain priors are considered in this work. Estimation can be carried out using a space-alternating generalized expectation-maximization (SAGE) algorithm; this leads to a novel type of NMF algorithm, whose convergence to a stationary point of the IS cost function is guaranteed. We also discuss the links between the IS divergence and other cost functions used in NMF, in particular, the Euclidean distance and the generalized Kullback-Leibler (KL) divergence. As such, we describe how IS-NMF can also be performed using a gradient multiplicative algorithm (a standard algorithm structure in NMF) whose convergence is observed in practice, though not proven. Finally, we report a furnished experimental comparative study of Euclidean-NMF, KL-NMF, and IS-NMF algorithms applied to the power spectrogram of a short piano sequence recorded in real conditions, with various initializations and model orders. Then we show how IS-NMF can successfully be employed for denoising and upmix (mono to stereo conversion) of an original piece of early jazz music. 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