Detection of coupling with linear and nonlinear synchronization measures for EEG

Abstract

There has been extensive research aimed at measuring synchronization to study the relationships between complex time series, such as electroencephalography (EEG). We compare six synchronization measures: the linear measures of cross-correlation, coherence and partial coherence, and three nonlinear similarity measures, namely correntropy, phase index and mutual information. We apply these measures to simulated data (unidirectionally coupled Hénon maps) to test the detection of nonlinear and nonstationary interdependence, including in the presence of noise. We also apply these measures to simulated EEG. The results suggest different measures have both good and bad features. No measure is the clear winner and no method completely fails. “Best measure” depends on the particular data and aim of the research.