Efficient and Robust Classification for Positive Definite Matrices with Wasserstein Metric

Abstract

Riemannian geometry methods are widely used to classify SPD (Symmetric Positives-Definite) matrices, such as covariances matrices of brain-computer interfaces. Common Riemannian geometry classification methods are based on Riemannian distance to compute the mean of matrices. The purpose of this paper is to propose different algorithms based on Bures-Wasserstein distance for computing the mean of SPD matrices. Combining two purposed BW algorithms, Inductive mean and Cheap mean, with the most common simple projection algorithm based on Riemannian distance, there are 6 kinds of mean algorithms tested. The results obtained in this paper include that Bures-Wasserstein simple projection mean algorithm has a better efficient and robust performance than the others.