基于可见性图的时间序列极值特征描述
Visibility graph-based characterization of extreme values in time series
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中文总结 AI 辅助
研究用可见性图刻画时间序列极值，该方法无需外部参数，可用于平稳和非平稳过程。对平稳过程利用节点度与数据值关系识别极值，对非平稳过程度排序指示重要性。经数据验证，结合标准方法可增强平稳序列极值刻画，对非平稳数据是有效替代，子采样可降成本保能力。
中文摘要 AI 辅助
复杂动力系统中观测变量常呈现极端波动，与长期平均值有显著偏差且影响重大。本文用可见性图刻画时间序列极值，该方法将时间序列非参数映射到网络，其拓扑结构继承原时间序列动力学特征。与基于阈值方法不同，无需引入外部参数，可用于平稳和非平稳过程。对平稳过程利用节点度与数据值的单调非线性关系识别极值，对非平稳过程度排序也能指示相对重要性。用合成和真实气候数据验证，结果表明结合标准方法与基于可见性图的检测可增强平稳时间序列极值刻画，对非平稳数据，可见性图是有效替代方法，还讨论了仅用峰值子采样时间序列可在降低计算成本的同时保持识别极值能力。
英文摘要
Complex dynamical systems often display extreme fluctuations of an observed variable that constitute significant deviations from the long-term average, and which are often associated with severe impacts on the system. By definition, extreme events are therefore usually explored from time series recordings. In this work, we characterize extreme values in time series using visibility graphs, a method that non-parametrically maps a time series onto a network, whose topological structure is known to inherit important characteristics of the original time series dynamics. Unlike threshold-based approaches, extreme values in this framework can be identified without the need to introduce external parameters and can be applied to time series generated by both stationary and nonstationary processes. For stationary processes, we exploit a known property of visibility graphs in which the degree of a node is monotonically and nonlinearly related to the corresponding data value. This nonlinear amplification enhances the contribution of large values while suppressing noise, while the monotonic relationship enables a direct ranking of data points according to node degree. This procedure identifies global extreme values and locally prominent ones. For nonstationary processes, the degree ranking in the visibility graph still provides a robust indicator of relative importance. We validate our findings with synthetic time series and with real climatological data. Our results show that extreme-value characterization in stationary time series is enhanced when combining standard methods with visibility-graph-based detection, whereas for nonstationary data, where conventional approaches are often ill-posed, visibility graphs provide an effective alternative. We discuss how sub-sampling the time series using only peak values preserves the ability to identify extreme values while reducing computational cost.
