Extending Nonnegative Matrix Factorization—A discussion in the context of multiple frequency estimation of musical signals

Nonnegative Matrix Approximation (NNMA) is a very well known technique of multivariate data analysis. However, in its basic form it provides very little control over its behaviour. This article explores possible extensions to this method in the context of multiple frequency estimation: using a parameterized distortion measure, enforcing harmonic structure on the basis matrix and introducing additional regularizations. We provide the reader with three regularizations useful for multiple pitch estimation and propose an objective way of evaluating the performance of NNMA-based pitch estimators. Finally, we use this evaluation method to train the parameters of our regularized harmonic NNMA and present the results.