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Optimal spectral transportation with application to music transcription
Rémi Flamary · Cédric Févotte · Nicolas Courty · Valentin Emiya

Tue Dec 06 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #75 #None

Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to quantify the adequacy of the decomposition compare the data and template entries frequency-wise. As such, small displacements of energy from a frequency bin to another as well as variations of timber can disproportionally harm the fit. We address these issues by means of optimal transportation and propose a new measure of fit that treats the frequency distributions of energy holistically as opposed to frequency-wise. Building on the harmonic nature of sound, the new measure is invariant to shifts of energy to harmonically-related frequencies, as well as to small and local displacements of energy. Equipped with this new measure of fit, the dictionary of note templates can be considerably simplified to a set of Dirac vectors located at the target fundamental frequencies (musical pitch values). This in turns gives ground to a very fast and simple decomposition algorithm that achieves state-of-the-art performance on real musical data.

Author Information

Rémi Flamary (École Polytechnique)
Cédric Févotte (CNRS)

Cédric Févotte is a CNRS research director with the Institut de Recherche en Informatique de Toulouse (IRIT). Previously, he has been a CNRS researcher at Laboratoire Lagrange (Nice, 2013-2016) & Télécom ParisTech (2007-2013), a research engineer at Mist-Technologies (the startup that became Audionamix, 2006-2007) and a postdoc at University of Cambridge (2003-2006). He holds MEng and PhD degrees in EECS from École Centrale de Nantes. His research interests concern statistical signal processing and machine learning, with particular interests in matrix factorisation, representation learning, source separation and recommender systems. He is currently the principal investigator of the European Research Council (ERC) project FACTORY (New paradigms for latent factor estimation, 2016-2022, 2M€).

Nicolas Courty (IRISA / University South Brittany)
Valentin Emiya (Aix-Marseille University)

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