Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review

By Massimiliano Zanin, Luciano Zunino, Osvaldo Anibal Rosso, David Papo. Entropy, 2012

615 citations recorded by the source corpus.

Entropy is a powerful tool for the analysis of time series, as it allows describing the probability distributions of the possible state of a system, and therefore the information encoded in it. Nevertheless, important information may be codified also in the temporal dynamics, an aspect which is not usually taken into account. The idea of calculating entropy based on permutation patterns (that is, permutations defined by the order relations among values of a time series) has received a lot of attention in the last years, especially for the understanding of complex and chaotic systems. Permutation entropy directly accounts for the temporal information contained in the time series; furthermore, it has the quality of simplicity, robustness and very low computational cost. To celebrate the tenth anniversary of the original work, here we analyze the theoretical foundations of the permutation entropy, as well as the main recent applications to the analysis of economical markets and to the understanding of biomedical systems.

Subfields: Economics and Econometrics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/76241784c14e30c8ab660ace3b1625df09d3f8f2

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Citations in the corpus

A multiscale permutation entropy based approach to select wavelet for fault diagnosis of ball bearings (2015, background): “At each time ‘s’ of a given a time series (Massimiliano et al., 2012) X ¼ ðx1, x2, x3 . . . xnÞ ð1Þ a vector composed of the mth subsequent values is constructed S! ðX ,X þ1, . . . ,X þðm 2Þ,X þðm 1ÞÞ ð2Þ where m is called embedding dimension and tells how much information is present in a vector…”
Complexity–entropy analysis of daily stream flow time series in the continental United States (2014, background): “These symbolic quantifiers were shown to be particularly useful for different purposes (Zanin et al. 2012) like characterizing stochastic processes (Rosso et al.”
Dispersion Entropy: A Measure for Time-Series Analysis (2016, methodology): “Although PE is conceptually simple and computationally fast [2], the method does not consider the mean value of amplitudes and differences between amplitude values [6].”