Multiple-order Non-negative Matrix Factorization for speech enhancement

Amongst the speech enhancement techniques, statistical models based on Non-negative Matrix Factorization (NMF) have received great attention. In a single channel configuration, NMF is used to describe the spectral content of both the speech and noise sources. As the number of components can have a crucial influence on separation quality, we here propose to investigate model order selection based on the variational Bayesian approximation to the marginal likelihood of models of different orders. To go further, we propose to use model averaging to combine several single-order NMFs and we show that a straightforward application of model averaging principles is inefficient as it turned out to be equivalent to model selection. We thus introduce a parameter to control the entropy of the model order distribution which makes the averaging effective. We also show that our probabilistic model nicely extends to a multiple-order NMF model where several NMFs are jointly estimated and averaged. Experiments are conducted on real data from the CHiME challenge and give an interesting insight on the entropic parameter and model order priors. Separation results are also promising as model averaging outperforms single-order model selection. Finally, our multiple-order NMF shows an interesting gain in computation time.