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When dealing with electro or magnetoencephalography records, many supervisedprediction tasks are solved by working with covariance matrices to summarizethe signals. Learning with these matrices requires using Riemanian geometry toaccount for their structure. In this paper, we propose a new method to dealwith distributions of covariance matrices and demonstrate its computationalefficiency on M/EEG multivariate time series. More specifically, we define aSliced-Wasserstein distance between measures of symmetric positive definitematrices that comes with strong theoretical guarantees. Then, we take advantageof its properties and kernel methods to apply this distance to brain-ageprediction from MEG data and compare it to state-of-the-art algorithms based onRiemannian geometry. Finally, we show that it is an efficient surrogate to theWasserstein distance in domain adaptation for Brain Computer Interfaceapplications.

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