A new metric based on pattern cross permutation for capturing interactions in complex time series

Identifying the coupling between variables in complex systems has emerged as a central focus of numerous studies. In this paper, we proposed modified spectral pattern cross permutation coefficient for recognizing both bivariate and multivariate coupling. Firstly, we transformed time series to frequency domain using Rihaczek distribution. By reconstructing attractor and computing point-weighted change patterns, the coupling strength is measured using modified inner composition alignment. Furthermore, we extended it to multivariate case and better characterize direct interactions between target variables. The method capture the global properties of dynamical system effectively and better characterize the positive and negative coupling relationships between complex series. Simulation experiments demonstrate the method's strong performance across multiple evaluation metrics. Finally, we applied the proposed method to analyze physiological signal coupling. By analyzing the EEG signals of patients with attention deficit hyperactivity disorder (ADHD), we identified abnormal coupling patterns related to frontal and temporal lobes, as well as distinctive Beta-band activity in ADHD patients. Moreover, the metrics derived from the proposed method effectively distinguished patients from healthy controls. In conclusion, this method offers a novel approach for identifying coupling interactions in complex systems and holds promise for applications in a wide range of research fields in the future.