Constrained Nonnegative Matrix Factorization with Applications to Music Transcription

Abstract

In this work we explore using nonnegative matrix factorization (NMF) for music transcription, as well as several other applications. NMF is an unsupervised learning method capable of finding a parts-based additive model of data. Since music has an additive property (each time point in a musical piece is composed of a sum of notes) NMF is a natural fit for analysis. NMF is able to exploit this additivity in order to factorize out both the individual notes and the transcription from an audio sample.

In order to improve the performance of NMF we apply different constraints to the model. We consider sparsity as well as piecewise smoothness with aligned breakpoints. We show the novelty of our method on real music data and demonstrate promising results which exceed the current state of the art. Other applications are also considered, such as instrument and speaker separation and handwritten character analysis.