Discrimination of coupling structures using causality networks from multivariate time series.

Measures of Granger causality on multivariate time series have been used to form the so-called causality networks. A causality network represents the interdependence structure of the underlying dynamical system or coupled dynamical systems, and its properties are quantified by network indices. In this work, it is investigated whether network indices on networks generated by an appropriate Granger causality measure can discriminate different coupling structures. The information based Granger causality measure of partial mutual information from mixed embedding (PMIME) is used to form causality networks, and a large number of network indices are ranked according to their ability to discriminate the different coupling structures. The evaluation of the network indices is done with a simulation study based on two dynamical systems, the coupled Mackey-Glass delay differential equations and the neural mass model, both of 25 variables, and three prototypes of coupling structures, i.e., random, small-world, and scale-free. It is concluded that the setting of PMIME combined with a network index attains high level of discrimination of the coupling structures solely on the basis of the observed multivariate time series. This approach is demonstrated to identify epileptic seizures emerging during electroencephalogram recordings.