利用Fisher-Shannon信息进行时间数据的高级分析：理论发展和在地球科学中的应用
Advanced analysis of temporal data using Fisher-Shannon information: theoretical development and application in geosciences
摘要：
复杂非线性时间序列在地球科学中普遍存在。量化这些数据的复杂性和非平稳性是一项具有挑战性的任务，需要先进的基于复杂性的探索工具来理解和可视化这些数据。本文讨论了Fisher-Shannon方法，从中可以获得复杂性度量和检测非平稳性，作为一种有效的数据探索工具。收集了与Fisher-Shannon测度相关的最新研究成果，提出了正单峰偏态分布的新解析公式。对合成数据和真实数据的案例研究表明了Fisher-Shannon方法的有效性，它可以应用于不同的领域，包括时间序列判别和生成用于聚类、建模和预测的时间序列特征。本文附带了Python和R库，用于对所提出的措施进行非参数估计。
英文摘要：
Complex non-linear time series are ubiquitous in geosciences. Quantifying complexity and non-stationarity of these data is a challenging task, and advanced complexity-based exploratory tool are required for understanding and visualizing such data. This paper discusses the Fisher-Shannon method, from which one can obtain a complexity measure and detect non-stationarity, as an efficient data exploration tool. The state-of-the-art studies related to the Fisher-Shannon measures are collected, and new analytical formulas for positive unimodal skewed distributions are proposed. Case studies on both synthetic and real data illustrate the usefulness of the Fisher-Shannon method, which can find application in different domains including time series discrimination and generation of times series features for clustering, modeling and forecasting. The paper is accompanied with Python and R libraries for the non-parametric estimation of the proposed measures.
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