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 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.

在本文中，我们为单变量时间序列的分类任务开发了拓扑数据分析方法。作为一个应用程序，我们在两个公共数据集上执行二元和三元分类任务，这些数据集由在压力和非压力条件下收集的生理信号组成。在我们使用信号的时间延迟嵌入并执行子窗口而不是使用固定长度的窗口之后，我们通过使用持久同源性来设计稳定的拓扑特征来实现我们的目标。我们使用的方法组合可以应用于任何单变量时间序列，并允许我们减少噪声并使用长窗口大小，而不会产生额外的计算成本。然后，我们在我们通过算法设计的特征上使用机器学习模型，以使用更少的特征获得更高的准确度。