Riemannian classification of covariance matrices coming from EEG signals

The goal of brain-computer interfaces (BCI) is to allow someone to interact with a device via his brain. A classic example of such a setting is a thought-controlled wheelchair. To do this, we need to capture information from the brain, which can be done via electroencephalography (EEG). We then must classify these signals: what does the person desire? Does the patient want to move forwards? Turn to the right? Turn to the left? This work is part of this framework. To work with these EEG signals, we will use their covariance matrices, which can help reducing the noise impact. A first step in the classification of the covariance matrices will be to reduce their dimension. This has been shown to improve the performances of the process. The set of covariance matrices has a particular structure that worth being considered, via the Riemannian geometry. In this thesis we extend or analyse further two existing methods. We then propose a new reduction method that is significantly faster than the two firsts, while conserving the classification performances.