Modeling Functional Networks via Piecewise-Stationary Graphical Models 1
In this chapter, we present statistical tools to model dynamic functional networks. As an application, we consider specifically scalp electroencephalogram (EEG) recordings during epileptic seizures. We model the multivariate time series by means of piecewise stationary copula Gaussian graphical models. Concretely, we first partition the time series into a number of stationary segments using a linear-complexity change point detection algorithm; the number of change points is determined automatically from data via an elbow rule. Next, we learn a copula Gaussian graphical model (with and without hidden variables) for each segment using tuning-free algorithms. As an illustration, we apply the proposed method to inferring functional brain networks from scalp EEG recorded during epileptic seizures. The proposed method is able to identify change points near the onset and termination of seizures. Kramer et al. (M. A. Kramer, U. T. Eden, E. D. Kolaczyk, R. Zepeda, E. N.Eskandar, and S. S. Cash, “Coalescence and fragmentation of cortical networks during focal seizures”, J Neurosci., vol.30, no. 30, pp. 10076–10085, 2010.) showed how functional networks evolve during the seizure via intracranial electrocorticogram (ECoG) recordings. They found that the networks are dense at the start and end of seizures, but sparse in the middle. Interestingly, although scalp EEG is different in nature from intracranial ECoG, the proposed method can extract similar patterns after considering hidden variables.