标题： 单变量时间序列的时间最优持久同调代表 显示英文标题

标题： Time-optimal persistent homology representatives for univariate time series

摘要： 持久同调（PH）是拓扑数据分析中的主要方法之一。 该领域的一个活跃研究方向是研究适当的PH代表概念，这些概念允许解释PH所提供的信息的含义，使其成为PH应用和研究其可解释性的重要问题。 计算最优PH代表是一个已知为NP难的问题，因此人们有兴趣开发在实践中可计算的特定上下文的最优性概念。 在这里，我们引入了时间变化数据的时间最优PH代表，使得能够提取在适当意义上时间接近的代表。 我们在准周期性合成时间序列以及来自气候模型的时间序列上展示了我们的方法，并表明我们的方法提供了比现有最优性概念（如长度最优PH代表）更适合这类问题的最优PH代表。 显示英文摘要

摘要： Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the information provided by PH, making it an important problem in the application of PH, and in the study of its interpretability. Computing optimal PH representatives is a problem that is known to be NP-hard, and one is therefore interested in developing context-specific optimality notions that are computable in practice. Here we introduce time-optimal PH representatives for time-varying data, allowing one to extract representatives that are close in time in an appropriate sense. We illustrate our methods on quasi-periodic synthetic time series, as well as time series arising from climate models, and we show that our methods provide optimal PH representatives that are better suited for these types of problems than existing optimality notions, such as length-optimal PH representatives.