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

TL;DR

This paper introduces a novel block-Toeplitz covariance matrix approach for linear discriminant analysis in EEG-based brain-computer interfaces, significantly improving classification accuracy and efficiency over existing methods.

Contribution

The paper proposes ToeplitzLDA, enforcing a block-Toeplitz structure on covariance matrices to better model stationarity, enhancing BCI classification performance and computational efficiency.

Findings

Up to 6 AUC points improvement over regularized LDA

81% reduction in spelling errors in BCI application

Robust performance despite increased feature dimensionality

Abstract

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