Multipitch Analysis with Harmonic Nonnegative Matrix Approximation

This paper presents a new approach to multipitch analysis by utilizing the Harmonic Nonnegative Matrix Approximation, a harmonically-constrained and penalized version of the Nonnegative Matrix Approximation (NNMA) method. It also includes a description of a note onset, offset and amplitude retrieval procedure based on that technique. Compared with the previous NNMA approaches, specific initialization of the basis matrix is employed – the basis matrix is initialized with zeros everywhere but at positions corresponding to harmonic frequencies of consequent notes of the equal temperament scale. This results in the basis containing nothing but harmonically structured vectors, even after the learning process, and the activity matrix’s rows containing peaks corresponding to note onset times and amplitudes. Furthermore, additional penalties of mutual uncorrelation and sparseness of rows are placed upon the activity matrix. The proposed method is able to uncover the underlying musical structure better than the previous NNMA approaches and makes the note detection process very straightforward.