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Entropy 2012, 14(8), 1553-1577; doi:10.3390/e14081553
Article

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

1,2,3,* , 4,5, 6,7 and 1
Received: 1 July 2012; in revised form: 10 August 2012 / Accepted: 21 August 2012 / Published: 23 August 2012
(This article belongs to the Special Issue Concepts of Entropy and Their Applications)
Download PDF [365 KB, uploaded 23 August 2012]
Abstract: 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.
Keywords: permutation entropy; forbidden patterns; Shannon entropy; econophysics; EEG; epilepsy permutation entropy; forbidden patterns; Shannon entropy; econophysics; EEG; epilepsy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Zanin, M.; Zunino, L.; Rosso, O.A.; Papo, D. Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy 2012, 14, 1553-1577.

AMA Style

Zanin M, Zunino L, Rosso OA, Papo D. Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review. Entropy. 2012; 14(8):1553-1577.

Chicago/Turabian Style

Zanin, Massimiliano; Zunino, Luciano; Rosso, Osvaldo A.; Papo, David. 2012. "Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review." Entropy 14, no. 8: 1553-1577.


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