Learning context invariant representations for EEG data

The goal of Brain-Computer Interfaces is to translate a user's brain activity into commands. To achieve this, the subject is equipped with sensors on their scalp that each record the electrical signals from a certain area of their brain using Electroencephalography (EEG). This EEG is a multivariate 0me series that contains very high-dimensional informa0on about brain activity. Unfortunately, EEGs are subject to a lot of variability, making it difficult to build a universal BCI. The goal of my PhD is to understand and tackle these variabilities. The most used representation of an EEG is its covariance matrix. As these matrices are symmetric positive definite (SPD), they live on a manifold that can be endowed with a Riemannian structure. This structure helps us better understand the intrinsic connections between the different SPD matrices in play. In my research, I am trying to build a probabilistic framework on the manifold of SPD matrices. The goal is to define and study a probability distribution that takes into account the Riemannian geometry of SPD matrices. Then, I could model a set of SPD matrices using this probability distribution and better understand how variabilities affect the covariance matrices derived from a BCI experiment.