Euler common spatial patterns for EEG classification

The technique of common spatial patterns (CSP) is a widely used method in the field of feature extraction of electroencephalogram (EEG) signals. Motivated by the fact that a cosine distance can enlarge the distance between samples of different classes, we propose the Euler CSP (e-CSP) for the feature extraction of EEG signals, and it is then used for EEG classification. The e-CSP is essentially the conventional CSP with the Euler representation. It includes the following two stages: each sample value is first mapped into a complex space by using the Euler representation, and then the conventional CSP is performed in the Euler space. Thus, the e-CSP is equivalent to applying the Euler representation as a kernel function to the input of the CSP. It is computationally as straightforward as the CSP. However, it extracts more discriminative features from the EEG signals. Extensive experimental results illustrate the discrimination ability of the e-CSP.