Riemannian Gaussian Distributions on the Space of Symmetric Positive Definite Matrices

Abstract

Data, which lie in the space Pm , of m×m symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications, including medical imaging, computer vision, and radar signal processing. An open challenge, for these applications, is to find a class of probability distributions, which is able to capture the statistical properties of data in Pm , as they arise in real-world situations. The present paper meets this challenge by introducing Riemannian Gaussian distributions on Pm . Distributions of this kind were first considered by Pennec in 2006. However, the present paper gives an exact expression of their probability density function for the first time i..