Time Series Classification via Topological Data Analysis

TL;DR

This paper introduces a topological data analysis approach for classifying univariate time series, leveraging persistent homology and subwindowing to improve accuracy and noise robustness in physiological signal classification.

Contribution

It develops a novel TDA-based feature engineering method for time series classification that reduces noise and computational cost, outperforming traditional approaches.

Findings

Achieved higher classification accuracy with fewer features.

Demonstrated robustness to noise in physiological signals.

Applicable to various univariate time series datasets.

Abstract

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.