Accounting for phase cancellations in non-negative matrix factorization using weighted distances

Techniques based on non-negative matrix factorization (NMF) have been successfully used to decompose a spectrogram of a music recording into a dictionary of templates and activations. While advanced NMF variants often yield robust signal models, there are usually some inaccuracies in the factorization since the underlying methods are not prepared for phase cancellations that occur when sounds with similar frequency are mixed. In this paper, we present a novel method that takes phase cancellations into account to refine dictionaries learned by NMF-based methods. Our approach exploits the fact that advanced NMF methods are often robust enough to provide information about how sound sources interact in a spectrogram, where they overlap, and thus where phase cancellations could occur. Using this information, the distances used in NMF are weighted entry-wise to attenuate the influence of regions with phase cancellations. Experiments on full-length, polyphonic piano recordings indicate that our method can be successfully used to refine NMF-based dictionaries