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Covariance matrices of noisy multichannel electroencephalogram time seriesdata are hard to estimate due to high dimensionality. In brain-computerinterfaces (BCI) based on event-related potentials and a linear discriminantanalysis (LDA) for classification, the state of the art to address this problemis by shrinkage regularization. We propose a novel idea to tackle this problemby enforcing a block-Toeplitz structure for the covariance matrix of the LDA,which implements an assumption of signal stationarity in short time windows foreach channel. On data of 213 subjects collected under 13 event-relatedpotential BCI protocols, the resulting 'ToeplitzLDA' significantly increasesthe binary classification performance compared to shrinkage regularized LDA (upto 6 AUC points) and Riemannian classification approaches (up to 2 AUC points).This translates to greatly improved application level performances, asexemplified on data recorded during an unsupervised visual speller application,where spelling errors could be reduced by 81% on average for 25 subjects. Asidefrom lower memory and time complexity for LDA training, ToeplitzLDA proved tobe almost invariant even to a twenty-fold time dimensionality enlargement,which reduces the need of expert knowledge regarding feature extraction.

Introducing Block-Toeplitz Covariance Matrices to Remaster Linear Discriminant Analysis for Event-related Potential Brain-computer Interfaces