A Generalised Directional Laplacian Distribution: Estimation, Mixture Models and Audio Source Separation

TL;DR

This paper introduces a new probability distribution called the Generalised Directional Laplacian Distribution (DLD) for modeling multidimensional sparse directional data, and applies it to underdetermined audio source separation.

Contribution

It proposes the DLD and its mixture model, enabling effective clustering and separation of sparse directional data, especially in audio applications.

Findings

DLD effectively models sparse directional data.

Mixture models improve source separation accuracy.

The approach offers a fast and stable solution for underdetermined audio separation.

Abstract

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.