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.

本文提出了一种新的概率分布，即广义方向拉普拉斯分布（DLD），以建模多维稀疏方向数据，该分布是拉普拉斯分布和 von Mises-Fisher 分布之间的混合物。作者探讨了将导出的 DLD 混合模型应用于聚类存在于欠定瞬时声混合物中的声源，该模型可以解决通用的 K x L (K<L) 欠定瞬时源分离问题，提供快速和稳定的解决方案。