# Classification of BCI-EEG based on augmented covariance matrix

arXiv: https://arxiv.org/abs/2302.04508 · HTML: https://mlsanity.com/paper/2302.04508/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 48 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [Manifold-regression to predict from MEG/EEG brain signals without source modeling](https://mlsanity.com/paper/1906.02687/) (2019)
- [Functional connectivity ensemble method to enhance BCI performance (FUCONE)](https://mlsanity.com/paper/2111.03122/) (2021)
- [Introducing Block-Toeplitz Covariance Matrices to Remaster Linear Discriminant Analysis for Event-related Potential Brain-computer Interfaces](https://mlsanity.com/paper/2202.02001/) (2022)
- [Phase space reconstruction from a biological time series. A PhotoPlethysmoGraphic signal a case study](https://mlsanity.com/paper/1910.05410/) (2019)

## Built on by (most cited first, 5 of 5)

- [The largest EEG-based BCI reproducibility study for open science: the MOABB benchmark](https://mlsanity.com/paper/2404.15319/) (2024)
- [Pseudo-online framework for BCI evaluation: A MOABB perspective](https://mlsanity.com/paper/2308.11656/) (2023)
- [Geometric Neural Network based on Phase Space for BCI-EEG decoding](https://mlsanity.com/paper/2403.05645/) (2024)
- [Enhancing Computational Efficiency of Motor Imagery BCI Classification with Block-Toeplitz Augmented Covariance Matrices and Siegel Metric](https://mlsanity.com/paper/2406.16909/) (2024)
- [Benchmarking Label-Revealed Online Updates for EEG BCI Decoding](https://mlsanity.com/paper/2610.07420/) (2026)

## Abstract (arXiv)

Objective: Electroencephalography signals are recorded as a multidimensional dataset. We propose a new framework based on the augmented covariance extracted from an autoregressive model to improve motor imagery classification. Methods: From the autoregressive model can be derived the Yule-Walker equations, which show the emergence of a symmetric positive definite matrix: the augmented covariance matrix. The state-of the art for classifying covariance matrices is based on Riemannian Geometry. A fairly natural idea is therefore to extend the standard approach using these augmented covariance matrices. The methodology for creating the augmented covariance matrix shows a natural connection with the delay embedding theorem proposed by Takens for dynamical systems. Such an embedding method is based on the knowledge of two parameters: the delay and the embedding dimension, respectively related to the lag and the order of the autoregressive model. This approach provides new methods to compute the hyper-parameters in addition to standard grid search. Results: The augmented covariance matrix performed noticeably better than any state-of-the-art methods. We will test our approach on several datasets and several subjects using the MOABB framework, using both within-session and cross-session evaluation. Conclusion: The improvement in results is due to the fact that the augmented covariance matrix incorporates not only spatial but also temporal information, incorporating nonlinear components of the signal through an embedding procedure, which allows the leveraging of dynamical systems algorithms. Significance: These results extend the concepts and the results of the Riemannian distance based classification algorithm.