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:在处理电或磁脉动记录时,许多受监督的预测任务是通过使用共变矩阵来总结信号来完成的。 与这些矩阵学习需要使用里马尼亚几何学来说明其结构。 在本文中, 我们提出了处理共变矩阵分布的新方法, 并在 M/ EEG 多变时间序列上展示其计算效率。 更具体地说, 我们定义了具有强烈理论保证的对称正对数确定矩阵测量方法之间的一个斜度- Wasserstein 距离。 然后, 我们利用其属性和内核方法, 将这一距离用于MEG 数据中的大脑年龄预测, 并将其与基于里曼尼亚几何测量方法的最新算法进行比较。 最后, 我们显示, 在脑计算机界面应用的域适应中, 它是一个高效的瓦列斯坦距离的代号。</s>