Introducing Block-Toeplitz Covariance Matrices to Remaster Linear Discriminant Analysis for Event-related Potential Brain-computer Interfaces
This work addresses a critical bottleneck in event-related potential brain-computer interfaces for users with motor impairments, offering a significant performance boost over existing methods.
The paper tackled the problem of estimating noisy covariance matrices in EEG-based brain-computer interfaces by enforcing a block-Toeplitz structure in linear discriminant analysis, resulting in up to 6 AUC point improvements in classification performance and an 81% reduction in spelling errors in an application.
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.