Regularized Partial Phase Synchrony Index Applied to Dynamical Functional Connectivity Estimation

We study the inference of conditional independence graph from the partial Phase Locking Value (PLV) index of mul-tivariate time series. A typical application is the inference of temporal functional connectivity from brain data. We extend the recently proposed time-varying graphical lasso to the measurement of partial locking values, yielding a sparse and temporally coherent dynamical graph that characterizes the evolution of the phase synchrony between each pair of signals. Cast as an optimization problem, we solve it using the alternating direction method of multipliers. The approach is validated on simulated Gaussian multivariate signals and Roessler oscillators. The potential of this regularized partial PLV is then illustrated on actual iEEG data during an epileptic seizure.