In this paper, we develop topological data analysis methods for classification tasks on univariate time series. As an application we perform binary and ternary classification tasks on two public datasets that consist of physiological signals collected under stress and non-stress conditions. We accomplish our goal by using persistent homology to engineer stable topological features after we use a time delay embedding of the signals and perform a subwindowing instead of using windows of fixed length. The combination of methods we use can be applied to any univariate time series and in this application allows us to reduce noise and use long window sizes without incurring an extra computational cost. We then use machine learning models on the features we algorithmically engineered to obtain higher accuracies with fewer features.

翻译：在本文中,我们为单向时间序列的分类任务开发了地形数据分析方法。作为一种应用,我们在两个由压力和非压力条件下收集的生理信号组成的公共数据集上执行二进制和永久分类任务。我们实现了我们的目标,在使用延迟时间嵌入信号并进行子窗口而不是使用固定长度的窗口后,我们用持久性同质法来设计稳定的地形特征。我们使用的方法组合可以适用于任何单向时间序列,在这个应用中,我们可以减少噪音,使用长窗口尺寸,而不产生额外的计算费用。然后我们用机器学习模型来研究我们用算法设计来获得更高精度的外观特征。