Structured non-negative matrix factorization with sparsity patterns

In this paper, we propose a novel algorithm for monaural blind source separation based on non-negative matrix factorization (NMF). A shortcoming of most source separation methods is the need for training data for each individual source. The algorithm proposed in this paper is able separate sources even when there is no training data for the individual sources.

The algorithm makes use of models trained on mixed signals and uses training data where more than one source is active at the time. This makes the algorithm applicable to situations where recordings of the individual sources are unavailable. The key idea is to construct a structure matrix that indicates where each source is active, and we prove that this structure matrix, combined with a uniqueness assumption, is sufficient to ensure that results are equivalent to training on isolated sources.

Our theoretical findings is backed up by simulations on music data that show that the proposed algorithm trained on mixed recordings performs as well as existing NMF source separation methods trained on solo recordings.