Permutation entropy: One concept, two approaches

Amigó, José M.; Keller, Karsten

doi:10.1140/epjst/e2013-01840-1

Cited by 34 publications

(26 citation statements)

References 69 publications

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“…We do not further discuss the implications of this fact here.). Using the frequency distribution of the possible order patterns for calculating a Shannon-type entropy leads to the notion of permutation entropy [31][32][33].…”

Section: Order-pattern Based Approachesmentioning

confidence: 99%

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Balasis

Donner

Potirakis

et al. 2013

Entropy

105

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This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

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Section: Order-pattern Based Approachesmentioning

confidence: 99%

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Balasis

Donner

Potirakis

et al. 2013

Entropy

105

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show abstract

“…On the one hand, permutation entropy is strongly related to KS entropy. It coincides with KS entropy for piecewise strictly monotone interval maps [4] and is not less than KS entropy for many dynamical systems [5][6][7] (see also [8,9] for some new results in this direction and [10] for the discussion of two approaches to the permutation entropy with respect to KS entropy). On the other hand, permutation entropy is estimated by empirical permutation entropy, which is conceptually simple and algorithmically fast [3,11].…”

Section: Motivationmentioning

confidence: 76%

Efficiently Measuring Complexity on the Basis of Real-World Data

Unakafova

Keller

2013

Entropy

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Permutation entropy, introduced by Bandt and Pompe, is a conceptually simple and well-interpretable measure of time series complexity. In this paper, we propose efficient methods for computing it and related ordinal-patterns-based characteristics. The methods are based on precomputing values of successive ordinal patterns of order d, considering the fact that they are "overlapped" in d points, and on precomputing successive values of the permutation entropy related to "overlapping" successive time-windows. The proposed methods allow for measurement of the complexity of very large datasets in real-time.

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“…Though implying the loss of nearly all the metric information, this often allows to extract some relevant information from a time series, in particular, when it comes from a complex system. For example, ordinal pattern analysis provides estimators of the Kolmogorov-Sinai entropy [18,21,22] of dynamical systems, measures of time series complexity [9,15,23], measures of coupling between time series [13,24] and estimators of parameters of stochastic processes [10,25], see also [12,26] for a review of applications to real-world time series. Methods of ordinal pattern analysis are invariant with respect to strictly-monotone distortions of time series [11], do not need information about range of measurements, and are computationally simple [14].…”

Section: Definition 2 Given a Stochastic Processmentioning

confidence: 99%