  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.
