Distinguishing different dynamics in electroencephalographic time series through a complex network approach

Abstract

In the context of dynamical systems, time series analysis is frequently used to identify the underlying nature of a phenomenon of interest from a sequence of observations and to forecast future outcomes. Recently, a map from time series to network has been proposed [4], allowing the use of network statistics to characterize time series. In this approach, time series quantiles are naturally mapped into nodes of a graph (here called Quantile Graph - QG). Therefore, the proposed map (here called QG algorithm) is able to capture and quantify features such as long range correlations or randomness present in the underlying dynamics of the original signal, making it a powerful tool for the analysis of nonlinear systems [4, 5]. As an illustration we applied the QG algorithm to the long standing problem of detecting the differences between electroencephalographic time series (EEG) of healthy and unhealthy subjects. The main goal is to find out how the differences in dynamics are reflected in the corresponding networks. Our results show that resulting networks display clear differences in topology, which are especially apparent on the small-world behaviour in the network associated with the healthy subject.