Nonnegative matrix partial co-factorization for drum source separation

We address a problem of separating drums from polyphonic music containing various pitched instruments as well as drums. Nonnegative matrix factorization (NMF) was successfully applied to spectrograms of music to learn basis vectors, followed by support vector machine (SVM) to classify basis vectors into ones associated with drums (rhythmic source) only and pitched instruments (harmonic sources). Basis vectors associated with pitched instruments are used to reconstruct drum-eliminated music. However, it is cumbersome to construct a training set for pitched instruments since various instruments are involved. In this paper, we propose a method which only incorporates prior knowledge on drums, not requiring such training sets of pitched instruments. To this end, we present nonnegative matrix partial co-factorization (NMPCF) where the target matrix (spectrograms of music) and drum-only-matrix (collected from various drums a priori) are simultaneously decomposed, sharing some factor matrix partially, to force some portion of basis vectors to be associated with drums only. We develop a simple multiplicative algorithm for NMPCF and show its usefulness empirically, with numerical experiments on real-world music signals.