Justin Dauwels, François Vialatte, Tomasz Rutkowski, Andrzej Cichocki
A novel approach to measure the interdependence of two time series is proposed, referred to as “stochastic event synchrony” (SES); it quantiﬁes the alignment of two point processes by means of the following parameters: time delay, variance of the timing jitter, fraction of “spurious” events, and average similarity of events. SES may be applied to generic one-dimensional and multi-dimensional point pro- cesses, however, the paper mainly focusses on point processes in time-frequency domain. The average event similarity is in that case described by two parameters: the average frequency offset between events in the time-frequency plane, and the variance of the frequency offset (“frequency jitter”); SES then consists of ﬁve pa- rameters in total. Those parameters quantify the synchrony of oscillatory events, and hence, they provide an alternative to existing synchrony measures that quan- tify amplitude or phase synchrony. The pairwise alignment of point processes is cast as a statistical inference problem, which is solved by applying the max- product algorithm on a graphical model. The SES parameters are determined from the resulting pairwise alignment by maximum a posteriori (MAP) estimation. The proposed interdependence measure is applied to the problem of detecting anoma- lies in EEG synchrony of Mild Cognitive Impairment (MCI) patients; the results indicate that SES signiﬁcantly improves the sensitivity of EEG in detecting MCI.