A Dirichlet Process Mixture Model for Spherical Data
Julian Straub, Jason S. Chang, Oren Freifeld, John W. Fisher · 2015
Directional data, naturally represented as points on the unit sphere, appear in many applications. However, unlike the case of Eu-clidean data, flexible mixture models on the sphere that can capture correlations, handle an unknown number of components and ex-tend readily to high-dimensional data have yet to be suggested. For this purpose we propose a Dirichlet process mixture model of Gaussian distributions in distinct tangent spaces (DP-TGMM) to the sphere. Impor-tantly, the formulation of the proposed model allows the extension of recent advances in ef-ficient inference for Bayesian nonparametric models to the spherical domain. Experiments on synthetic data as well as real-world 3D surface normal and 20-dimensional semantic word vector data confirm the expressiveness and applicability of the DP-TGMM. 1