Global Permutation Entropy
This is an incremental improvement for researchers analyzing time series complexity, offering a more comprehensive measure.
The paper tackles the limitation of standard permutation entropy by introducing Global Permutation Entropy (GPE), which considers all possible patterns of a given length, including non-consecutive ones, and demonstrates its effectiveness on synthetic datasets by revealing structural information not accessible through the standard method.
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'.