Novel graph permutation entropy measures outperform classical methods in modeling brain functional connectivity and clustering brain subsystems.
Permutation entropy (PE) has been widely used to assess the complexity of time series and, in this context, has been applied to the analysis of various types of signals. In this paper, we advance the theory related to PE by defining joint entropy, mutual information, and quadratic dependence measures based on so-called graph permutation entropies. Similarly to their original counterparts commonly employed in information theory, the proposed measures aim to quantify the interdependence between time series. This is validated by applying the measures to the modeling of brain functional connectivity, using electromagnetic resonance imaging data selected from the Human Connectome Project. Our results are supported by performance scores that evaluate the precision of clustering operations through which known brain subsystems are detected in healthy subjects. In this context, we conclude that the introduced measures may achieve better performance than those obtained using previously proposed measures. • Novel PE-based joint entropy and mutual information measures are introduced. • Graph permutation entropy is used to capture multivariate signal dependencies. • Proposed measures outperform Pearson correlation and classical mutual information. • Brain functional connectivity is modeled using rs-fMRI data from 300 HCP subjects. • Graph permutation mutual information achieves the best clustering of brain subsystems.
Lima et al. (Thu,) studied this question.