Time Series Classification via Topological Data Analysis
This work provides an incremental method for time series classification, potentially benefiting researchers working with physiological signals and other univariate time series data.
This paper introduces a method for classifying univariate time series using topological data analysis. By applying persistent homology to time delay embeddings and subwindowing, the authors achieved higher classification accuracies with fewer features on physiological signal datasets related to stress detection.
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.