Efficient model selection for speech enhancement using a deflation method for Nonnegative Matrix Factorization

We present a deflation method for Nonnegative Matrix Factorization (NMF) that aims to discover latent components one by one in order of importance. To do so we perform a series of individual decompositions, each of which stands for a deflation step. In each deflation we obtain a dominant component and a nonnegative residual, and then the residual is further used as an input to the next deflation in case we want to extract more components. With the help of the proposed additional inequality constraint on the residual during the optimization, the accumulated latent components at any given deflation step can approximate the input to some degree, whereas NMF with an inaccurate rank assumption often fail to do so. The proposed method is beneficial if we need efficiency in deciding the model complexity from unknown data. We derive multiplicative update rules similar to those of regular NMF to perform the optimization. Experiments on online speech enhancement show that the proposed deflation method has advantages over NMF: namely a scalable model structure, reusable parameters across decompositions, and resistance to permutation ambiguity.