Dee Algar Shannon, Corrêa Débora C, Walker David M
Department of Mathematics and Statistics, University of Western Australia, Crawley 6009, Australia.
Chaos. 2021 Dec;31(12):123117. doi: 10.1063/5.0073247.
This work outlines a pipeline for time series analysis that incorporates a measure of similarity not previously applied between homological summaries. Specifically, the well-established, but disparate, methods of persistent homology and TrAnsformation Cost Time Series (TACTS) are combined to provide a metric for tracking dynamics via changing homological features. TACTS allows subtle changes in dynamics to be accounted for, gives a quantitative output that can be directly interpreted, and is tunable to provide several complementary perspectives simultaneously. Our method is demonstrated first with known dynamical systems and then with a real-world electrocardiogram dataset. This paper highlights inadequacies in existing persistent homology metrics and describes circumstances where TACTS can be more sensitive and better suited to detecting a variety of regime changes.
这项工作概述了一种用于时间序列分析的流程，该流程纳入了一种以前未在同源性总结之间应用的相似性度量。具体而言，将成熟但不同的持久同源性方法和变换成本时间序列（TACTS）方法相结合，以提供一种通过变化的同源特征来跟踪动态的度量。TACTS能够考虑动态中的细微变化，给出可直接解释的定量输出，并且可以进行调整以同时提供多个互补视角。我们的方法首先在已知动态系统上进行了演示，然后在一个真实世界的心电图数据集上进行了演示。本文突出了现有持久同源性度量的不足之处，并描述了TACTS在哪些情况下可以更敏感且更适合检测各种状态变化。
