Symbolic convergent cross mapping based on permutation mutual information

In this paper, we extend convergent cross mapping (CCM) and propose symbolic CCM (SCCM), which uses mutual information based on permutation pattern instead of Pearson correlation coefficient to estimate cross-mapping ability. We numerically demonstrate that SCCM is a robust method for quantifying information flow between time series in chaotic systems, even under the influence of noises. Using the method, we analyze the multichannel EEG signals of ADHD children and control children, and identify the differences between the two groups of subjects with reliable results.