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On Rényi Permutation Entropy.

Tim Gutjahr1, Karsten Keller1

  • 1Institute of Mathematics, University of Lübeck, D-23562 Lübeck, Germany.

Entropy (Basel, Switzerland)
|January 21, 2022
PubMed
Summary
This summary is machine-generated.

This study explores Rényi permutation entropies, a novel variant of permutation entropy. These entropies, parameterized by q, generalize Shannon entropy and connect to other complexity measures.

Keywords:
Kolmogorov–Sinai entropyRényi entropypermutation entropy

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Area of Science:

  • Complexity Science
  • Information Theory
  • Nonlinear Dynamics

Background:

  • Permutation entropy quantifies system dynamics via ordinal patterns.
  • Rényi entropies offer a generalized framework for information quantification.
  • Existing literature has explored modifications of permutation entropy.

Purpose of the Study:

  • To discuss the concept of Rényi permutation entropies.
  • To analyze the dependence on the parameter q.
  • To explore connections to established entropy measures.

Main Methods:

  • Definition of Rényi permutation entropy based on Rényi entropy.
  • Parameterization using the non-negative real number q.
  • Comparative analysis with Shannon entropy (q=1).

Main Results:

  • Rényi permutation entropy is introduced as a generalization.
  • The parameter q controls the entropy measure.
  • Connections to Kolmogorov-Sinai entropy and symbolic correlation integral are established.

Conclusions:

  • Rényi permutation entropy provides a flexible tool for analyzing complex systems.
  • This framework unifies different entropy measures.
  • Further research can leverage this concept for deeper insights into system dynamics.