Measurement of information transfer based on phase increment transfer entropy

The construction of time series networks in complex systems facilitates the investigation of information interaction mechanisms among subsystems. As widely used causal relationship measurement techniques, Granger causality (GC) is applicable to linear coupling, and information loss is a problem with transfer entropy based on permutation. In order to reasonably analyze the evolution of information transfer between nonlinear signals, we develop a novel causality inference method. In this paper, phase increment transfer entropy (PITE) is proposed, which performs increment symbolic processing on the phase series of signals, taking into account both sign and magnitude. PITE displays effectiveness in simulation experiments, and is more robust than baseline models that measure phase series information transfer of signals. Furthermore, PITE provided evidence that the information transfer between electroencephalogram (EEG) signals of healthy individuals and patients with Attention Deficit Hyperactivity Disorder (ADHD) differs. K-Nearest Neighbors (KNN) is utilized for categorizing subjects based on the causality network, demonstrating the effectiveness of PITE for assessing ADHD and quantifying brain information transfer. The proposed method will provide a novel idea for EEG-based disease research, and help to develop a broader understanding of causality networks.