  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.
