Les factorisations en matrices non-négatives. Approches contraintes et probabilistes, application à la transcription automatique de musique polyphonique.

Abstract : Automatic transcription of music consists in producing a symbolic representation of a piece of music (for instance a MIDI file) from the raw audio content. Monodic music transcription is now well handled, but the case of polyphonic music is still a widely open question. Eigenvalue decomposition and singular value decomposition are classical linear algebra techniques, used in a wide range of signal processing applications. They allow to represent efficiciently the observed data by using a limited number of elementary atoms. Unlike other signal representation techniques, those atoms are not searched among a pre-defined dictionary, but learnt from the data itself. Non-negative matrix factorization (NMF) is a similar technique from linear algebra, which reduces the rank while providing atoms with exclusively positive entries, more easy to interpret. It provides simultaneously a dictionary extracted from the data, and the decomposition of the same data on this dictionary. This thesis is devoted to a detailed theoretical and experimental study of this method. It aims at several goals: improving the performance of NMF-based music transcription systems, enhancing the semantics of the produced mid-level representations, and controlling theoretical and practical properties of both state-of-the-art and original algorithms which were implemented during the thesis.
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Nancy Bertin. Les factorisations en matrices non-négatives. Approches contraintes et probabilistes, application à la transcription automatique de musique polyphonique.. Traitement du signal et de l'image [eess.SP]. Télécom ParisTech, 2009. Français. ⟨tel-00472896⟩

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