Novel measures of pairwise time series interdependence using graph permutation entropies: An application to brain...

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.