Posted on 22 March 2010

Paper details:

Nonnegative matrix factorization (NMF) has become a popular tool for discovering structure in a variety of signals. When applied to a musical audio signal, NMF builds a set of dictionary atoms that represent the individual musical sources in the signal. To perform music transcription, we map the learned dictionary atoms to musical notes and beats.

The basic formulation of NMF has the notable disadvantage that sources may require more than a single dictionary atom in order to be approximated accurately. For example, one note played by a violin may require multiple dictionary atoms to be accurately represented due to the vibrato induced by the performer. In the presence of many other musical sources, the correspondence between atoms becomes unclear.

In this paper, we introduce three new update rules to enforce dependence among dictionary atoms by incorporating co-occurrence constraints into NMF. These co-occurrence constraints have shown to be useful for describing sources with multiple, co-occurring dictionary atoms by grouping similar atoms into sets. The proposed rules are conceptually simple, easy to implement, and effective for describing sources using multiple dictionary atoms.