Global Permutation Entropy

Abhijeet Avhale, Joscha Diehl, Niraj Velankar, Emanuele Verri
8/27/2025
cs.LGcs.IT

Official code: AThreeH1/Global-Permutation-Entropy (0 stars, last commit 2025-08-27).

Abstract

Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment to a permutation and computing the frequency distribution of these permutations, Shannon Entropy is then applied to quantify the series' complexity. We introduce Global Permutation Entropy (GPE), a novel index that considers all possible patterns of a given length, including non-consecutive ones. Its computation relies on recently developed algorithms that enable the efficient extraction of full permutation profiles. We illustrate some properties of GPE and demonstrate its effectiveness through experiments on synthetic datasets, showing that it reveals structural information not accessible through standard permutation entropy. We provide a Julia package for the calculation of GPE at `https://github.com/AThreeH1/Global-Permutation-Entropy'.

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Code Implementations(1)

AThreeH1/Global-Permutation-EntropyOfficial100%

Complexity measure for ordinal patterns

00Julia, PythonAug 26, 20251 years ago

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Cite this paper

@article{avhale2025global,
  title  = {Global Permutation Entropy},
  author = {Abhijeet Avhale and Joscha Diehl and Niraj Velankar and Emanuele Verri},
  year   = {2025},
  eprint = {2508.19955},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2508.19955v1}
}

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