Complexity of Continuous Functions and Novel Technologies for Classification of Multi-channel EEG Records

Abstract

A multi-channel EEG signal is a time series for which there is no universally recognized mathematical model. The analysis and classification of such and many similar complex signals with an unknown generation mechanism requires the development of model-free technologies. We propose a fundamentally novel approach to the problem of classification for vector time series of arbitrary nature and, in particularly, for multi-channel EEG. The proposed approach is based on our theory of the $\epsilon$-complexity of continuous vector-functions. This theory is in line with the general idea of A.N. Kolmogorov on a complexity of an individual object. The theory of the $\epsilon$-complexity enables us to effectively characterize the complexity of an individual continuous vector-function. Such a characterization does not depend on the generation mechanism of a continuous vector-function and is its “intrinsic” property. The main results of the $\epsilon$-complexity theory are given in the paper. Based on this theory, the principles of new technologies of classification for multi-channel EEG signals are formulated. The proposed technologies do not use any assumptions about the mechanisms of EEG signal generation and, therefore, are model-free. We present the results of the first applications of new technologies to the analysis of real EEG and fNIRS data. We conducted two experiments with data obtained from a study of people with schizophrenia and autism spectrum disorder, and we obtained classification accuracy up to 85% for the first one and up to 88.9% for the second.