A Generalised Directional Laplacian Distribution: Estimation, Mixture Models and Audio Source Separation
This work addresses the problem of clustering sound sources in underdetermined audio mixtures for audio processing applications, presenting an incremental hybrid method.
The authors tackled the problem of modeling sparse directional data by proposing a novel probability distribution, the Generalised Directional Laplacian Distribution, and applied it to audio source separation, offering a fast and stable solution for underdetermined instantaneous mixtures.
Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalised Directional Laplacian Distribution (DLD) is a hybrid between the Laplacian distribution and the von Mises-Fisher distribution. The distribution's parameters are estimated using Maximum-Likelihood Estimation over a set of training data points. Mixtures of Directional Laplacian Distributions (MDLD) are also introduced in order to model multiple concentrations of sparse directional data. The author explores the application of the derived DLD mixture model to cluster sound sources that exist in an underdetermined instantaneous sound mixture. The proposed model can solve the general K x L (K<L) underdetermined instantaneous source separation problem, offering a fast and stable solution.