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.

第一代脑机接口（BCI）对多通道脑电图（EEG）信号进行了分类，并通过优化的空间滤波器对其进行了增强。第二代根据直接距离算法（例如，最小距离与最大距离）直接对基于脑电信号估计的协方差矩阵进行了分类。 -黎曼平均（MDRM）。分类结果的差异取决于所选的黎曼距离或散度，其定义和参考实现方式散布在广泛的数学文献中。本文回顾了所有黎曼距离和散度，以处理协方差矩阵，并实现了与BCI约束兼容的实现。在稳态视觉诱发电位（SSVEP）数据集上评估使用不同指标的影响，评估类的中心和分类准确性。黎曼方法嵌入了处理脑电数据的关键属性。在离线和在线设置中，Riemannian类的中心都优于欧几里得类。就分类精度而言，某些黎曼距离和散度具有更好的性能，而另一些具有吸引人的计算效率。