On the use of the beta divergence for musical source separation

Non-negative Tensor Factorisation based methods have found use in the context of musical sound source separation. These techniques require the use of a suitable cost function to determine the optimal factorisation, and most work has focused on the use of the generalised Kullback-Liebler divergence, and more recently the Itakura-Saito divergence. These divergences can be regarded as limiting cases of the parameterised Beta divergence. This paper looks at the use of the Beta Divergence in the context of musical source separation with a view to determining an optimal value of Beta for this problem. This is considered for both magnitude and power spectrograms. In an effort to avoid potential local minima in the Beta divergence, the use of a "tempered" Beta Divergence is also explored. Also presented are the update equations for the generalised non-negative tensor factorisation model described in this paper which were previously unpublished.