Music self-similarity modeling using augmented nonnegative matrix factorization of block and stripe patterns

Abstract

Self-similarity matrices have been widely used to analyze the sectional form of music signals, e.g. enabling the detection of parts such as verse and chorus in popular music. Two main types of structures often appear in self-similarity matrices: rectangular blocks of high similarity and diagonal stripes off the main diagonal that represent recurrent sequences. In this paper, we introduce a novel method to model both the block and stripe-like structures in self-similarity matrices and to pull them apart from each other. The model is an extension of the nonnegative matrix factorization, for which we present multiplicative update rules based on the generalized Kullback-Leibler divergence. The modeling power of the proposed method is illustrated with examples, and we demonstrate its application to the detection of sectional boundaries in music.