Robust averaging of covariances for EEG recordings classification in motor imagery brain-computer interfaces

The estimation of covariance matrices is of prime importance to analyze the distribution of multivariate signals. In motor imagery based brain-computer interfaces (MI-BCI), covariance matrices play a central role in the extraction of features from recorded electroencephalograms (EEGs), therefore, estimating covariances properly is crucial for EEG classification. The paper discusses algorithms to average sample covariance matrices (SCMs) for the selection of the reference matrix in tangent space mapping (TSM) based MI-BCI. Tangent space mapping is a powerful method of feature extraction and strongly depends on the selection of a reference covariance matrix. In general, the observed signals may include outliers, therefore, taking the geometric mean of SCMs as the reference matrix may not be the best choice. In order to deal with the effects of outliers, robust estimators have to be used. In particular, we discuss and test the use of geometric medians and trimmed averages (defined on the basis of several metrics) as robust estimators. The main idea behind trimmed averages is to eliminate those data that exhibit the largest distance from the average covariance calculated on the basis of all available data. The results of the experiments show that, while the geometric medians show little differences from conventional methods in terms of classification accuracy in the classification of electroencephalographic recordings, the trimmed averages show a significant improvement for all subjects.