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• Zunino, L
• Rosso, O
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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

Massimiliano Zanin ^1,2,3,* , Luciano Zunino ^4,5 , Osvaldo A. Rosso ^6,7  and David Papo ¹

¹ Centre for Biomedical Technology, Polytechnic University of Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain ² Faculdade de Ciências e Tecnologia, Departamento de Engenharia Electrotécnica, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal ³ Innaxis Foundation & Research Institute José Ortega y Gasset 20, 28006 Madrid, Spain ⁴ Centro de Investigaciones Ópticas (CONICET La Plata - CIC) C.C. 3, 1897 Gonnet, Argentina ⁵ Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina ⁶ LaCCAN/CPMAT - Instituto de Computação, Universidade Federal de Alagoas, BR 104 Norte km 97, 57072-970 Maceió, Alagoas, Brazil ⁷ Laboratorio de Sistemas Complejos, Facultad de Ingeniería, Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires, Argentina

* Author to whom correspondence should be addressed.

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 Full-Text [365 KB, uploaded 23 August 2012 13:48 CEST]

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

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