提出全局排列熵，捕捉时间序列中非连续模式的复杂性。
Global Permutation Entropy
- 扩展传统排列熵，纳入所有可能的非连续模式
- 在合成数据上揭示了传统方法无法检测的结构信息
- 适合研究复杂系统动态特征的研究者使用
排列熵由Bandt和Pompe提出，是一种广泛用于实值时间序列的复杂性度量方法，基于固定长度连续片段内数值的相对顺序。通过将每个片段标准化为一个排列并计算这些排列的频率分布，再应用香农熵来量化序列的复杂性。本文提出全局排列熵（GPE），一种新指标，考虑给定长度下所有可能的排列模式，包括非连续模式。其计算依赖于近期发展的算法，可高效提取完整的排列轮廓。我们展示了GPE的一些性质，并通过合成数据集实验验证了其有效性，结果表明它能揭示传统排列熵无法获取的结构信息。相关Julia代码已在GitHub开源：https://github.com/AThreeH1/Global-Permutation-Entropy。
原文摘要 · Abstract (English)
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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