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

arXiv: https://arxiv.org/abs/2202.02001 · HTML: https://mlsanity.com/paper/2202.02001/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 65 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 6 of 6)

- [EEGNet: A Compact Convolutional Network for EEG-based Brain-Computer Interfaces](https://mlsanity.com/paper/1611.08024/) (2016)
- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [Transfer Learning in Brain-Computer Interfaces](https://mlsanity.com/paper/1512.00296/) (2015)
- [A Plug&Play P300 BCI Using Information Geometry](https://mlsanity.com/paper/1409.0107/) (2014)
- [Learning from Label Proportions in Brain-Computer Interfaces: Online Unsupervised Learning with Guarantees](https://mlsanity.com/paper/1701.07213/) (2017)
- [Efficient Hierarchical Bayesian Inference for Spatio-temporal Regression Models in Neuroimaging](https://mlsanity.com/paper/2111.01692/) (2021)

## Built on by (most cited first, 4 of 4)

- [Classification of BCI-EEG based on augmented covariance matrix](https://mlsanity.com/paper/2302.04508/) (2023)
- [UMM: Unsupervised Mean-difference Maximization](https://mlsanity.com/paper/2306.11830/) (2023)
- [Review of Deep Representation Learning Techniques for Brain-Computer Interfaces and Recommendations](https://mlsanity.com/paper/2405.19345/) (2024)
- [Exploring new territory: Calibration-free decoding for c-VEP BCI](https://mlsanity.com/paper/2403.15521/) (2024)

## Abstract (arXiv)

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.