Model-oriented non-negative matrix factorization based music separation

Music separation is performed by learning the parameters that could best interpret the given piece of music under specific criteria. In this paper, we illustrate this by modelling a music part using the source-filter model. We made two improvements to this linear representation: Moving-Average method is used to give each partial a distinct Attack-Sustain-Release pattern and Gaussian function is used to build peaks in every excitation, leading to a unified linear representation of both pitched and unpitched components, e.g., Noise generator can be set in our excitation model which shares the same structure with harmonic components. Also, numerical stability of multiplicative update rules, which is the intrinsic flaw of the classical Nonnegative Matrix Factorization algorithm is addressed in our approach. We use both median filter and cut-off to sparsify and smooth the result to get rid of overhead introduced by a constraint in the cost function.