Alexandra Piryatinska, Associate Professor, Department of Mathematics, San Francisco State University
A methodology for quantitative classification of mental states into two groups using EEG records is proposed. This methodology is based on the theory of the ε-complexity of continuous functions which is extended here to the case of vector-functions. This extension permits us to handle multichannel EEG records. The essence of the methodology is to use the ε-complexity coefficients as features for classification of different types of vector-functions representing EEG-records corresponding to different mental states. The methodology contains two steps. The first step is an estimation of the ε-complexity coefficients of the original signal and its finite differences. The second step is utilizing of Random Forest (RF) or Support Vector Machine (SVM) classifiers.We demonstrated the performance of our method on simulated data. We also applied it to the problem of classification of multichannel-EEG records related to a group of healthy adolescents (39 subjects) and a group of adolescents with schizophrenia (45 subjects). We found that the random forest classifier provides a superior result. In particular, out-of-bag accuracy in the case of RF was 85.3\%. Using 10-fold cross-validation (CV), RF gave an average accuracy of 84.5\% on a test set, whereas SVM gave an accuracy of 81.07\%. We note that the highest accuracy on CV was 89.3\%. To compare our method with the classical approach, we performed classification using the spectral features. In this case, the best performance was achieved using seven-dimensional feature space, with an average accuracy of 83.6\%. The obtained results indicate the effectiveness of the proposed methodology.
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