Constructing Time-Varying Directed EEG Network by Multivariate Nonparametric Dynamical Granger Causality

Time-varying directed electroencephalography (EEG) network is the potential tool for studying the dynamical causality among brain areas at a millisecond level; which conduces to understanding how our brain effectively adapts to information processing, giving inspiration to causality- and brain-inspired machine learning. Currently, its construction still mainly relies on the parametric approach such as multivariate adaptive autoregressive (MVAAR), represented by the most widely used adaptive directed transfer function (ADTF). Restricted by the model assumption, the corresponding performance largely depends on the MVAAR modeling which usually encounters difficulty in fitting complex spectral features. In this study, we proposed to construct EEG directed network with multivariate nonparametric dynamical Granger causality (mndGC) method that infers the causality of a network, instead, in a data-driven way directly and therefore avoids the trap in the model-dependent parametric approach. Comparisons between mndGC and ADTF were conducted both with simulation and real data application. Simulation study demonstrated the superiority of mndGC both in noise resistance and capturing the instantaneous directed network changes. When applying to the real motor imagery (MI) data set, distinguishable network characters between left- and right-hand MI during different MI stages were better revealed by mndGC. Our study extends the nonparametric causality exploration and provides practical suggestions for the time-varying directed EEG network analysis.