# Global Permutation Entropy

arXiv: https://arxiv.org/abs/2508.19955 · HTML: https://mlsanity.com/paper/2508.19955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 13 references that are in the map.
- First posted on arXiv 27 Aug 2025.

## Builds on (most cited first, 3 of 3)

- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Counting Small Permutation Patterns](https://mlsanity.com/paper/1911.01414/) (2019)
- [Counting Permutation Patterns with Multidimensional Trees](https://mlsanity.com/paper/2407.04971/) (2024)

## Abstract (arXiv)

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'.