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Correctly identifying interaction patterns from multivariate time series presents an important step in functional network construction. In this context, the widespread use of bivariate statistical association measures often results in a false identification of links because strong similarity between two time series can also emerge without the presence of a direct interaction due to intermediate mediators or common drivers. In order to properly distinguish such direct and indirect links 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 multi-channel EEG recordings to investigate possible differences in coordinated alpha band activity among macroscopic brain regions in resting states with eyes open (EO) and closed (EC) conditions. Specifically, we find that direct connections typically correspond to close spatial neighbors 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, our approach leads to a significant reduction in the number of indirect connections and thereby contributes to a better understanding of the alpha band desynchronization phenomenon in the EO state.
Functional network representations have recently gained considerable interest in the study of real-world spatially extended dynamical systems like the Earth’s climate or the human brain. In a vast fraction of cases, the existence of network links has been established by resorting to the presence of strong bivariate statistical associations as suggested by symmetric association measures like classical linear (Pearson) correlations. This methodology, however, disregards two relevant aspects: the directionality of dynamical interactions between pairs of actors and the complexity of mutual (synergistic or antagonistic) inter-dependencies that can lead to the spurious identification of connections in case of, for example, common drivers or directed chain-like coupling configurations. In order to address both aspects, various approaches based on nonlinear time series analysis have been developed in the last few years, most of which assume the presence of a continuous temporal variability pattern. However, in the context of event-like data like spikes in neural activity or climate extremes, there still exists a considerable gap in suitable methodologies for unravelling the complex web of directed interactions from multivariate time series. The present work introduces partial event coincidence analysis as a new approach and studies its applicability to different types of model systems as well as real-world EEG data.
