Decomposition and classification of electroencephalography data

This thesis is about linear and multi-linear analyses of electroencephalography (EEG) data and classification of estimated EEG sources. One contribution consists of an automatic classification method for independent components (ICs) of EEG data and a freely available implementation as an EEGLab plug-in, “IC Classification into Multiple Artefact Classes” (IC_MARC). Four artefact classes (blinks, heart beats, lateral eye movements, and muscle contractions), a neural class, and a mixed class (representing none or a mix of the other classes) were considered. We showed that classification is possible between subjects within studies over all classes. When generalising across studies a high classification rate of neural vs. non-neural ICs was retained but the multi-class performance dropped. In another study, we used IC_MARC to compare the ability to separate artefactual from neural sources of six linear decomposition methods. This study showed that high-pass filtering data at high cut-off frequencies improved artefact removal performances in an Event-Related Desynchronisation setting, providing similar performances of the three included Independent Component Analysis variants. IC_MARC was also used to inspect effects of artefacts on motor imagery based Brain-Computer Interfaces (BCIs) in two studies, where removing artefactual ICs had little performance impact. Finally, we investigated multi-linear classification on single trials of EEG data, proposing a rigorous optimisation approach. To enforce orthonormality of projection matrices, objective functions quantifying class discrimination were optimised on a cross-product of Stiefel (orthonormal matrix) manifolds. Supervised feature extraction outperformed unsupervised methods, but the choice of supervised method mattered less. We suggested completions of methods to include both PARAFAC and Tucker structures. The two structures provided similar performances, making the more interpretable PARAFAC models appealing.