Randomized Matrix Decompositions and Exemplar Selection in Large Dictionaries for Polyphonic Piano Transcription

Abstract

Non-negative matrix factorization has been shown to be powerful for modelling audio signals. Many useful applications based on NMF, including musical source separation and polyphonic transcription, have been presented in the field of music information retrieval. The multiplicative update rules for making inference on the NMF model are quite simple and practical; however, they do not scale up well with the increasing size of the dictionary matrices. In this study, we develop efficient approaches based on randomized matrix decompositions and exemplar selection that can easily handle very large dictionary matrices that can be encountered in real applications. We apply our methods on the transcription of polyphonic piano music. The results show that by only retaining of a large dictionary matrix, we still get high performance in terms of objective measures.