Review of Riemannian Distances and Divergences, Applied to SSVEP-based BCI

The firstgeneration of brain-computer interfaces (BCI) classifies multi-channel electroencephalographic (EEG) signals, enhanced by optimized spatial filters.The second generation directly classifies covariance matrices estimated on EEG signals, based on straightforward algorithms such as the minimum-distance-to-Riemannian-mean (MDRM). Classification results vary greatly depending on the chosen Riemannian distance or divergence, whose definitions and reference implementations are spread across a wide mathematical literature. This paper reviews all the Riemannian distances and divergences to process covariance matrices, with an implementation compatible with BCI constraints. The impact of using different metrics is assessed on a steady-state visually evoked potentials (SSVEP) dataset, evaluating centers of classes and classification accuracy. Riemannian approaches embed crucial properties to process EEG data. The Riemannian centers of classes outperform Euclidean ones both in offline and online setups. Some Riemannian distances and divergences have better performances in terms of classification accuracy, while others have appealing computational efficiency.