Permutation group entropy: A new route to complexity for real-valued processes

Amigó, José M.; Dale, Roberto; Tempesta, Piergiulio

doi:10.1063/5.0113335

Cited by 4 publications

(2 citation statements)

References 53 publications

(93 reference statements)

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“…Outside thermodynamics, entropy finds a significant application within information theory as a tool to characterize the complexity of a deterministic or random process generating a time series. More precisely, we can associate with a time series an ordinal representation formed by all ordinal patterns of length

assigned [ 17 ]. Assuming that all different patterns are allowed for a process, we have

, and each pattern i will occur with a probability of

.…”

Section: Why Extensivitymentioning

confidence: 99%

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Group Structure as a Foundation for Entropies

Jensen,

Tempesta

2024

Entropy

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Entropy can signify different things. For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced, and it can be difficult to ascertain their respective importance and merits. Here, we consider entropy in an abstract sense, as a functional on a probability space, and we review how being able to handle the trivial case of non-interacting systems, together with the subtle requirement of extensivity, allows for a systematic classification of the functional form.

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assigned [ 17 ]. Assuming that all different patterns are allowed for a process, we have

, and each pattern i will occur with a probability of

.…”

Section: Why Extensivitymentioning

confidence: 99%

“…To discuss this fundamental application of group entropies, we start with a brief review of the ordinal analysis of time-series data. We follow the discussion and notations in [ 17 , 26 , 27 ]. Consider the time series

where t represents a discrete time and

.…”

Section: Group Entropy Theory and Data Analysismentioning

confidence: 99%

Group Structure as a Foundation for Entropies

Jensen,

Tempesta

2024

Entropy

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A review of symbolic dynamics and symbolic reconstruction of dynamical systems

Hirata

Amigó

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Discretizing a nonlinear time series enables us to calculate its statistics fast and rigorously. Before the turn of the century, the approach using partitions was dominant. In the last two decades, discretization via permutations has been developed to a powerful methodology, while recurrence plots have recently begun to be recognized as a method of discretization. In the meantime, horizontal visibility graphs have also been proposed to discretize time series. In this review, we summarize these methods and compare them from the viewpoint of symbolic dynamics, which is the right framework to study the symbolic representation of nonlinear time series and the inverse process: the symbolic reconstruction of dynamical systems. As we will show, symbolic dynamics is currently a very active research field with interesting applications.

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Ordinal pattern-based complexity analysis of high-dimensional chaotic time series

Kottlarz

Parlitz

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The ordinal pattern-based complexity–entropy plane is a popular tool in nonlinear dynamics for distinguishing stochastic signals (noise) from deterministic chaos. Its performance, however, has mainly been demonstrated for time series from low-dimensional discrete or continuous dynamical systems. In order to evaluate the usefulness and power of the complexity–entropy (CE) plane approach for data representing high-dimensional chaotic dynamics, we applied this method to time series generated by the Lorenz-96 system, the generalized Hénon map, the Mackey–Glass equation, the Kuramoto–Sivashinsky equation, and to phase-randomized surrogates of these data. We find that both the high-dimensional deterministic time series and the stochastic surrogate data may be located in the same region of the complexity–entropy plane, and their representations show very similar behavior with varying lag and pattern lengths. Therefore, the classification of these data by means of their position in the CE plane can be challenging or even misleading, while surrogate data tests based on (entropy, complexity) yield significant results in most cases.

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Permutation group entropy: A new route to complexity for real-valued processes

Cited by 4 publications

References 53 publications

Group Structure as a Foundation for Entropies

Group Structure as a Foundation for Entropies

A review of symbolic dynamics and symbolic reconstruction of dynamical systems

Ordinal pattern-based complexity analysis of high-dimensional chaotic time series

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