Towards Complex Nonnegative Matrix Factorization with the Beta-Divergence

Complex nonnegative matrix factorization (NMF) is a powerful tool for decomposing audio spectrograms while accounting for some phase information in the time-frequency domain. While its estimation was originally based on the Euclidean distance, in this paper we propose to extend it to any beta-divergence, a family of functions widely used in audio to estimate NMF. To this end, we introduce the beta-divergence in a heuristic fashion within a phase-aware probabilistic model. Estimating this model results in performing an NMF with Itakura-Saito (IS) divergence on a quantity called the phase-corrected posterior power of the sources, which is both phase-dependent and nonnegative-valued. Therefore, we replace IS with the beta-divergence, so that the factorization uses an optimal distortion metric and remains phase-aware. Even though by doing so we loose theoretical convergence guarantees, the resulting algorithm demonstrates its potential for an audio source separation task, where it outperforms previous complex NMFs approaches.

source separation

• separation