Notes on Nonnegative Tensor Factorization of the Spectrogram for Audio Source Separation: Statistical Insights and Towards Self-Clustering of the Spatial Cues

Nonnegative tensor factorization (NTF) of multichannel spectrograms under PARAFAC structure has recently been proposed by Fitzgerald et al as a mean of performing blind source separation (BSS) of multichannel audio data. In this paper we investigate the statistical source models implied by this approach. We show that it implicitly assumes a nonpoint-source model contrasting with usual BSS assumptions and we clarify the links between the measure of fit chosen for the NTF and the implied statistical distribution of the sources. While the original approach of Fitzgeral et al requires a posterior clustering of the spatial cues to group the NTF components into sources, we discuss means of performing the clustering within the factorization. In the results section we test the impact of the simplifying nonpoint-source assumption on underdetermined linear instantaneous mixtures of musical sources and discuss the limits of the approach for such mixtures.