Spectral Representation of EEG Data using Learned Graphs with Application to Motor Imagery Decoding

Electroencephalography (EEG) data entail a complex spatiotemporal structure that reflects ongoing organization of brain activity. Characterization of the spatial patterns is an indispensable step in numerous EEG processing pipelines within the setting of brain-computer interface systems as well as cognitive neuroscience. We present an approach for transforming EEG data into a spectral representation by using the harmonic basis of a graph structure that is learned from the data. The harmonic basis is obtained by integrating principles from graph learning and graph signal processing (GSP). First, we learn subject-specific graphs from each subjects EEG data. Second, by eigendecomposition of the normalized Laplacian matrix of each subjects graph, an orthonormal basis is obtained onto which each EEG map can be decomposed, providing a spectral representation of the data. We show that energy of the EEG maps is strongly associated with low frequency components of the learned basis, reflecting the smooth topography of EEG maps as expected. As a proof-of-concept for this alternative view of EEG data, we consider the task of decoding two-class motor imagery (MI) data. To this aim, the spectral representations are first mapped into a discriminative subspace for differentiating two-class data using a projection matrix obtained by the Fukunaga-Koontz transform (FKT), providing a minimal subspace from which features are extracted. An SVM classifier is then trained and tested on the resulting features to differentiate MI classes. The proposed method is evaluated on Dataset IVa of the BCI Competition III and its performance is compared to using features extracted from a subject-specific functional connectivity matrix and four state-of-the-art alternative methods. Experimental results indicate the superiority of the proposed method over alternative approaches, reflecting the added benefit of i) decomposing EEG data using data-driven, subject-specific harmonic bases, and ii) accounting for class-specific temporal variations in spectral profiles via the FKT. The proposed method and results underline the importance of integrating spatial and temporal characteristics of EEG signals in extracting features that can more powerfully differentiate MI classes.