A Bayes optimal matrix-variate LDA for extraction of spatio-spectral features from EEG signals

Classification of mental states from electroencephalogram (EEG) signals is used for many applications in areas such as brain-computer interfacing (BCI). When represented in the frequency domain, the multichannel EEG signal can be considered as a two-directional spatio-spectral data of high dimensionality. Extraction of salient features using feature extractors such as the commonly used linear discriminant analysis (LDA) is an essential step for the classification of these signals. However, multichannel EEG is naturally in matrix-variate format, while LDA and other traditional feature extractors are designed for vector-variate input. Consequently, these methods require a prior vectorization of the EEG signals, which ignores the inherent matrix-variate structure in the data and leads to high computational complexity. A matrix-variate formulation of LDA have previously been proposed. However, this heuristic formulation does not provide the Bayes optimality benefits of LDA. The current paper proposes a Bayes optimal matrix-variate formulation of LDA based on a matrix-variate model for the spatio-spectral EEG patterns. The proposed formulation also provides a strategy to select the most significant features among the different rows and columns.