A probabilistic view on Riemannian machine learning models for SPD matrices

Abstract

The goal of this paper is to show how different machine learning tools on the Riemannian manifold P_d of Symmetric Positive Definite (SPD) matrices can be united under a probabilistic framework. For this, we will need several Gaussian distributions defined on P_d. We will show how popular classifiers on P_d can be reinterpreted as Bayes Classifiers using these Gaussian distributions. These distributions will also be used for outlier detection and dimension reduction. By showing that those distributions are pervasive in the tools used on P_d, we allow for other machine learning tools to be extended to P_d.

Tasks

Reproductions