Determining a Suitable Desired Factors for Nonnegative Matrix Factorization in Polyphonic Music Transcription

Abstract

Nonnegative matrix factorization (NMF) is a technique that factorizes a given matrix V into W and H: NMF(Vmn )rarrWmr Hrn . NMF has been applied to various problem domains. So far there has been no fixed rule to select the number of NMF factoring (i.e. the desired factor r). In music transcription, the value r has the semantic of the desired musical line. If the r is not set correctly, the transcription output will not be accurate. In this paper, we present a tactic to get around this issue. We found that by concatenating an input audio stream with another audio stream with prior knowledge of r, where r ges the number of musical lines; we are guaranteed to get the correct number of musical lines in the transcription output. In our approach, NMF is applied to extract musical notes from FFT coefficients extracted from input polyphonic audio streams. The output from our experiment is encouraging and we hope to explore this further in the future.