TY - GEN
T1 - A tempering approach for Itakura-Saito non-negative matrix factorization. With application to music transcription
AU - Bertin, Nancy
AU - Févotte, Cédric
AU - Badeau, Roland
PY - 2009/9/23
Y1 - 2009/9/23
N2 - In this paper we are interested in non-negative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. Previous work has demonstrated the relevance of this cost function for the decomposition of audio power spectrograms. This is in particular due to its scale invariance, which makes it more robust to the wide dynamics of audio, a property which is not shared by other popular costs such as the Euclidean distance or the generalized Kulback-Leibler (KL) divergence. However, while the latter two cost functions are convex, the IS divergence is not, which makes it more prone to convergence to irrelevant local minima, as observed empirically. Thus, the aim of this paper is to propose a tempering scheme that favors convergence of IS-NMF to global minima. Our algorithm is based on NMF with the beta-divergence, where the shape parameter beta acts as a temperature parameter. Results on both synthetical and music data (in a transcription context) show the relevance of our approach.
AB - In this paper we are interested in non-negative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. Previous work has demonstrated the relevance of this cost function for the decomposition of audio power spectrograms. This is in particular due to its scale invariance, which makes it more robust to the wide dynamics of audio, a property which is not shared by other popular costs such as the Euclidean distance or the generalized Kulback-Leibler (KL) divergence. However, while the latter two cost functions are convex, the IS divergence is not, which makes it more prone to convergence to irrelevant local minima, as observed empirically. Thus, the aim of this paper is to propose a tempering scheme that favors convergence of IS-NMF to global minima. Our algorithm is based on NMF with the beta-divergence, where the shape parameter beta acts as a temperature parameter. Results on both synthetical and music data (in a transcription context) show the relevance of our approach.
KW - Beta divergence
KW - Itakura-Saito (IS) divergence
KW - Music transcription
KW - Non-negative matrix factorization (NMF)
U2 - 10.1109/ICASSP.2009.4959891
DO - 10.1109/ICASSP.2009.4959891
M3 - Conference contribution
AN - SCOPUS:70349202189
SN - 9781424423545
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 1545
EP - 1548
BT - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing - Proceedings, ICASSP 2009
T2 - 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009
Y2 - 19 April 2009 through 24 April 2009
ER -