Automatic sleep scoring through classifiers defined on the manifold of SPD matrices

The scoring of a subject’s sleep stages from electroencephalographic (EEG) signals is a costly process. As such, many approaches to its automation have been proposed, including ones based on Deep Learning. However, said approaches have yet to attain a level of performance good enough for use in clinical settings, in part due to the high variability between EEG recordings, and the challenges inherent to the classification of signals recorded in different environments.In this thesis, we tackle this issue through a novel angle, by representing each epoch within our EEG signals as a timeseries of covariance matrices. Said matrices, although a common tool for EEG analysis in Brain-Computer Interfaces (BCI are not typically utilized in sleep stage scoring.Covariance matrices tend to be symmetric positive definite (SPD), with the set of SPD matrices forming a non-Euclidean Riemannian manifold. As such, a Euclidean analysis of SPD matrices leads to computational artifacts, hence the need to utilize Riemannian operations instead, i.e. operations that respect the curvature of the manifold.To do so, we develop a Transformer-style deep neural network, modified to allow for the analysis of sequences of SPD matrices while still conforming to the structure of the manifold. From there, we demonstrate both the high level of performance of this approach, and its resilience to dataset changes.