Enhancing Computational Efficiency of Motor Imagery BCI Classification with Block-Toeplitz Augmented Covariance Matrices and Siegel Metric

TL;DR

This paper proposes an improved method for motor imagery BCI classification that leverages the mathematical properties of Block-Toeplitz covariance matrices and the Siegel metric, enhancing computational efficiency while maintaining accuracy.

Contribution

It introduces a novel approach that exploits the Block-Toeplitz structure of covariance matrices within Riemannian geometry, improving efficiency over traditional augmented covariance methods.

Findings

Achieves similar classification accuracy to ACM and state-of-the-art methods.

Significantly improves computational efficiency for real-time applications.

Validated using the MOABB framework with within-session evaluation.

Abstract

Electroencephalographic signals are represented as multidimensional datasets. We introduce an enhancement to the augmented covariance method (ACM), exploiting more thoroughly its mathematical properties, in order to improve motor imagery classification.Standard ACM emerges as a combination of phase space reconstruction of dynamical systems and of Riemannian geometry. Indeed, it is based on the construction of a Symmetric Positive Definite matrix to improve classification. But this matrix also has a Block-Toeplitz structure that was previously ignored. This work treats such matrices in the real manifold to which they belong: the set of Block-Toeplitz SPD matrices. After some manipulation, this set is can be seen as the product of an SPD manifold and a Siegel Disk Space.The proposed methodology was tested using the MOABB framework with a within-session evaluation procedure. It achieves a similar classification performance to ACM, which is typically better than -- or at worse comparable to -- state-of-the-art methods. But, it also improves consequently the computational efficiency over ACM, making it even more suitable for real time experiments.