Partial Event Coincidence Analysis For Distinguishing Direct And Indirect Coupling Configurations In Functional Network Construction

Functional network is an important class of Complex network.Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction.In previous work,bivariate statistical association methods have been widely used for network structure inference.However,strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers.So bivariate measures often result in a false identification of links.In order to properly distinguish such direct and indirect coupling configurations for the special case of event-like data,we present here a new generalization of event coincidence analysis to a partial version thereof,which is aimed at excluding possible transitive effects of indirect couplings.Using coupled chaotic systems and stochastic processes on two generic coupling topologies(star and chain configuration),we demonstrate that the proposed methodology allows for the correct identification of indirect interactions.Subsequently,we apply our partial event coincidence analysis to multichannel EEG recordings to investigate possible differences in coordinated alpha band activity among macroscopic brain regions in resting states with eyes open(EO)and closed conditions(EC).Specifically,we find that direct connections typically correspond to close spatial neighbours while indirect ones often reflect longer-distance connections mediated via other brain regions.In the EC state,connections in the frontal parts of the brain are enhanced as compared to the EO state,while the opposite applies to the posterior regions.In general,the method proposed in this paper can well distinguish direct and indirect coupling in both numerical simulation and real data analysis,which reduces the misjudgment in network structure inference,and provides an improved new method for functional network construction.