Online algorithms for Nonnegative Matrix Factorization with the Itakura-Saito divergence

Augustin Lefèvre (1) , Francis Bach (2) , Cédric Févotte (3)

1 SIERRA - Statistical Machine Learning and Parsimony
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 LTCI - Laboratoire Traitement et Communication de l'Information

Nonnegative matrix factorization (NMF) is now a common tool for audio source separation. When learning NMF on large audio databases, one major drawback is that the complexity in time is O(FKN) when updating the dictionary (where (F;N) is the dimension of the input power spectrograms, and K the number of basis spectra), thus forbidding its application on signals longer than an hour. We provide an online algorithm with a complexity of O(FK) in time and memory for updates in the dictionary. We show on audio simulations that the online approach is faster for short audio signals and allows to analyze audio signals of several hours.

Keywords: matrix factorization; online algorithms; Bregman divergences; audio source separation; machine learning

Domains: Machine Learning [stat.ML]; Signal and Image processing; Signal and Image Processing

Augustin Lefèvre, Francis Bach, Cédric Févotte. Online algorithms for Nonnegative Matrix Factorization with the Itakura-Saito divergence. 2011. ⟨hal-00602050⟩