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Entropy 2015, 17(6), 3595-3620; doi:10.3390/e17063595

Entropies from Markov Models as Complexity Measures of Embedded Attractors

1
Department of Systems Engineering, Universidad de Antioquia, Cll 70 No. 52-21, Medellín, Colombia
2
Center for Biomedical Technologies, Universidad Politécnica de Madrid, Crta. M40, km. 38, Pozuelode Alarcón, 28223, Madrid, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Received: 19 March 2015 / Revised: 27 May 2015 / Accepted: 28 May 2015 / Published: 2 June 2015
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [691 KB, uploaded 2 June 2015]   |  

Abstract

This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes. View Full-Text
Keywords: complexity analysis; hidden Markov models; principal curve; entropy measures complexity analysis; hidden Markov models; principal curve; entropy measures
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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. (CC BY 4.0).

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Arias-Londoño, J.D.; Godino-Llorente, J.I. Entropies from Markov Models as Complexity Measures of Embedded Attractors. Entropy 2015, 17, 3595-3620.

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