# Global Permutation Entropy

## TL;DR

This paper introduces Global Permutation Entropy (GPE), a new complexity measure for time series that considers all possible permutation patterns, including non-consecutive ones, providing deeper structural insights than standard permutation entropy.

## Contribution

The paper presents GPE, a novel permutation entropy variant that accounts for all pattern types, supported by efficient algorithms and a Julia implementation.

## Key findings

- GPE captures structural information missed by standard permutation entropy.
- Experiments on synthetic data demonstrate GPE's effectiveness.
- GPE reveals new insights into time series complexity.

## 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'.