Estimating Permutation Entropy Variability via Surrogate Time Series

Abstract

In the last decade permutation entropy (PE) has become a popular tool to analyze the degree of randomness within a time series. In typical applications, changes in the dynamics of a source are inferred by observing changes of PE computed on different time series generated by that source. However, most works neglect the crucial question related to the statistical significance of these changes. The main reason probably lies in the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty. In this paper we propose a method to overcome this issue by using generation of surrogate time series. The analysis conducted on both synthetic and experimental time series shows the reliability of the approach, which can be promptly implemented by means of widely available numerical tools. The method is computationally affordable for a broad range of users.

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen–Shannon Distance

“…Even when the attenuation of the alpha waves over the human posterior cortex in the EO condition is a well-known recognized fact for almost a century [14], different approaches have more recently been proposed to obtain an improved discrimination and classification of these baseline brain states [2,7,[15][16][17][18][19]. It has been found, for example, that different entropy measures (permutation entropy, approximate entropy, multiscale entropy, spatial permutation entropy) achieve higher values in the EO condition compared with the EC one [2,16,18,20,21]. This can be explained by the increasing disorder and desynchronization of brain activity due to visual information receiving and processing [16].…”