Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals

TL;DR

This paper introduces a new Sliced-Wasserstein distance for symmetric positive definite matrices, enabling efficient analysis of M/EEG signals and improving brain-age prediction and domain adaptation in BCI applications.

Contribution

It proposes a novel Sliced-Wasserstein distance for covariance matrices with theoretical guarantees, facilitating faster computation and application to brain signal analysis.

Findings

Effective in brain-age prediction from M/EEG data

Improves computational efficiency over traditional Riemannian methods

Enhances domain adaptation in Brain-Computer Interface tasks

Abstract

When dealing with electro or magnetoencephalography records, many supervised prediction tasks are solved by working with covariance matrices to summarize the signals. Learning with these matrices requires using Riemanian geometry to account for their structure. In this paper, we propose a new method to deal with distributions of covariance matrices and demonstrate its computational efficiency on M/EEG multivariate time series. More specifically, we define a Sliced-Wasserstein distance between measures of symmetric positive definite matrices that comes with strong theoretical guarantees. Then, we take advantage of its properties and kernel methods to apply this distance to brain-age prediction from MEG data and compare it to state-of-the-art algorithms based on Riemannian geometry. Finally, we show that it is an efficient surrogate to the Wasserstein distance in domain adaptation for Brain Computer Interface applications.