Chung Yu-Min, Hu Chuan-Shen, Lo Yu-Lun, Wu Hau-Tieng
Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC, United States.
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan.
Front Physiol. 2021 Mar 1;12:637684. doi: 10.3389/fphys.2021.637684. eCollection 2021.
Persistent homology is a recently developed theory in the field of algebraic topology to study shapes of datasets. It is an effective data analysis tool that is robust to noise and has been widely applied. We demonstrate a general pipeline to apply persistent homology to study time series, particularly the instantaneous heart rate time series for the heart rate variability (HRV) analysis. The first step is capturing the shapes of time series from two different aspects-the persistent homologies and hence persistence diagrams of its sub-level set and Taken's lag map. Second, we propose a systematic and computationally efficient approach to summarize persistence diagrams, which we coined . To demonstrate our proposed method, we apply these tools to the HRV analysis and the sleep-wake, REM-NREM (rapid eyeball movement and non rapid eyeball movement) and sleep-REM-NREM classification problems. The proposed algorithm is evaluated on three different datasets via the cross-database validation scheme. The performance of our approach is better than the state-of-the-art algorithms, and the result is consistent throughout different datasets.
持久同调是代数拓扑领域中最近发展起来的一种用于研究数据集形状的理论。它是一种有效的数据分析工具，对噪声具有鲁棒性，并且已经得到了广泛应用。我们展示了一个通用的流程，用于应用持久同调来研究时间序列，特别是用于心率变异性（HRV）分析的瞬时心率时间序列。第一步是从两个不同方面捕捉时间序列的形状——其下水平集的持久同调以及由此得到的持久图和塔克滞后映射。其次，我们提出了一种系统且计算高效的方法来总结持久图，我们将其命名为 。为了展示我们提出的方法，我们将这些工具应用于HRV分析以及睡眠 - 清醒、快速眼动 - 非快速眼动（快速眼球运动和非快速眼球运动）和睡眠 - 快速眼动 - 非快速眼动分类问题。通过跨数据库验证方案在三个不同数据集上对所提出的算法进行评估。我们方法的性能优于现有算法，并且在不同数据集上的结果是一致的。
