Quantifying the direct and indirect interactions for EEG signals by using detrended permutation mutual information

In this paper, we extend detrended cross-correlations analysis (DCCA) and introduce a novel method called detrended permutation mutual information (DPMI) by utilizing information-theoretic tools. The main mechanism of this paper is to use the invariance of the nonlinear monotonic transformation and robustness in permutation mutual information (PMI), which solves the limitations of DCCA only applicable to linear measurements and enhances the robustness of DPMI to noise. We compare the performance of DPMI with DCCA on multifractal binomial measures and Hénon maps for testing the effectiveness of the new method. By analyzing EEG signals obtained from children with attention deficit hyperactivity disorder (ADHD) as well as healthy children, we demonstrate that DPMI surpasses DCCA in processing physiological signals. Furthermore, we conclude that DPMI is more effective in distinguishing between different states within distinct groups. Given that EEG signals in physiological systems are associated with other channel signals, we propose a method called partial DPMI (PDPMI) that combines partial-correlation technique with DPMI. PDPMI can further reveal the direct interactions between two considered signals by eliminating potential influences from other unconsidered signals. In summary, PDPMI serves as a complementary perspective to DPMI, enhancing our understanding in the interactive structure of physiological network.