We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change point detection framework. The key rationale is that change points are likely to be associated with changes in geometry behind the data generating process. While the applications of topological data analysis to change point detection are potentially very broad, in this paper we primarily focus on integrating topological concepts with the existing nonparametric methods for change point detection. In particular, the proposed new geometry-oriented approach aims to enhance detection accuracy of distributional regime shift locations. Our simulation studies suggest that integration of topological data analysis with some existing algorithms for change point detection leads to consistently more accurate detection results. We illustrate our new methodology in application to the two closely related environmental time series datasets -ice phenology of the Lake Baikal and the North Atlantic Oscillation indices, in a research query for a possible association between their estimated regime shift locations.

中文翻译：

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利用拓扑数据分析的力量来检测变化点

我们在变化点检测框架中引入了一种基于拓扑数据分析的新兴工具的面向几何的新方法。关键的基本原理是变化点可能与数据生成过程背后的几何变化有关。虽然拓扑数据分析在变点检测中的应用可能非常广泛，但在本文中，我们主要关注将拓扑概念与现有的变点检测非参数方法相结合。特别是，所提出的新的面向几何的方法旨在提高分布状态转移位置的检测精度。我们的模拟研究表明，将拓扑数据分析与一些现有的变化点检测算法相结合，可以得到始终如一的更准确的检测结果。