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

TL;DR

This paper introduces an online algorithm for Nonnegative Matrix Factorization with the Itakura-Saito divergence, significantly reducing computational complexity and enabling analysis of long-duration audio signals.

Contribution

The authors develop an online NMF algorithm with O(FK) complexity, improving scalability for large audio datasets compared to traditional methods.

Findings

Online algorithm is faster for short signals

Enables analysis of several-hour-long audio signals

Reduces computational complexity from O(FKN) to O(FK)

Abstract

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.