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.

翻译：在处理脑电图或脑磁图记录时，许多监督预测任务通过协方差矩阵对信号进行汇总来解决。利用这些矩阵进行学习需要借助黎曼几何来考虑其结构。本文提出了一种处理协方差矩阵分布的新方法，并证明了其在M/EEG多元时间序列上的计算效率。具体而言，我们定义了对称正定矩阵测度之间的切片瓦瑟斯坦距离，该距离具有坚实的理论保证。随后，我们利用其性质与核方法，将该距离应用于基于MEG数据的脑龄预测，并与基于黎曼几何的最先进算法进行比较。最后，我们证明在脑机接口应用的领域自适应中，它是瓦瑟斯坦距离的有效替代方法。