Detection of coupling with linear and nonlinear synchronization measures for EEG

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, and to simulated EEG. No measure fails, none is the clear winner, all measures have advantages and disadvantages. 'Best measure' depends on the research aims and data. The tests selected here for EEG research recommend correntropy as the preferred measure.