@ygerAveragingCovarianceMatrices2015

Averaging covariance matrices for EEG signal classification based on the CSP: An empirical study (2015)

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1 Abstract

This paper presents an empirical comparison of covariance matrix averaging methods for EEG signal classification. Indeed, averaging EEG signal covariance matrices is a key step in designing brain-computer interfaces (BCI) based on the popular common spatial pattern (CSP) algorithm. BCI paradigms are typically structured into trials and we argue that this structure should be taken into account. Moreover, the non-Euclidean structure of covariance matrices should be taken into consideration as well. We review several approaches from the literature for averaging covariance matrices in CSP and compare them empirically on three publicly available datasets. Our results show that using Riemannian geometry for averaging covariance matrices improves performances for small dimensional problems, but also the limits of this approach when the dimensionality increases.

2 NOTES

This is an empirical paper where the authors evaluate the use of different distances to calculate a mean covariance matrix for each class, which is then used with CSP to classify three datasets. Then the Karcher mean is minimized using: Euclidean (${\delta }_e$), Log-Euclidean (${\delta }_l$), AIRM (${\delta }_r$ and ${\delta }_r^2$), and a $\beta$-divergence. The following table has their results, and, overall, the AIRM achieved the best accuracies, however, as the authors state, once the number of electrodes increase it is less favored. Also, the best geometry choice seems to be subject-dependent. It a classic paper, there is not much to it but is well written and a direct application, but nothing substantial for nowadays.