In recent years, Transformer-based auto-attention mechanisms have been successfully applied to the analysis of a variety of context-reliant data types, from texts to images and beyond, including data from non-Euclidean geometries. In this paper, we present such a mechanism, designed to classify sequences of Symmetric Positive Definite matrices while preserving their Riemannian geometry throughout the analysis. We apply our method to automatic sleep staging on timeseries of EEG-derived covariance matrices from a standard dataset, obtaining high levels of stage-wise performance.

翻译：近年来，基于Transformer的自注意力机制已成功应用于从文本到图像等多种依赖上下文的数据类型分析，包括来自非欧几里得几何的数据。本文提出了一种基于自注意力机制的模型，旨在对对称正定矩阵序列进行分类，并在整个分析过程中保持其黎曼几何结构。我们将该方法应用于标准数据集中基于脑电图协方差矩阵时间序列的自动睡眠分期任务，在各分期上均取得了高性能表现。