The objective of this work is to demonstrate an Electroencephalogram (EEG) experiment that fits a Brain-Computer-Interface (BCI) and can handle the problem of "inter-session variability", that its meaning is lack of stationarity of the EEG signals that is recorded from a specific subject in different times (different "sessions").
In this work, several mathematic techniques from the field of Riemannian Geometry were examined with the ambition to improve those algorithms in order to bridge over the gap between measurements taken in different days and contribute to the research and development of a robust BCI for ALS patients.
The solution that was selected is an algorithm called Parallel Transport (PT). In the first stage, the assumption was that the covariance matrices used for the implementation are full rank (Symmetric Positive Definite SPD), but after the algorithm's implementation and the deduction that it deals with the problem yet not sufficiently, it has been decided to change this assumption and implement a PT algorithm that is based on the assumption that the covariance matrices aren't full rank (Symmetric Positive Semi Definite SPSD). This implementation led to significant improvement of the results comparing to the first ones.