Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

TL;DR

This paper explores transformer-based ECG classification using Koopman operator and wavelet features, demonstrating that Koopman features with a tuned EDMD dictionary outperform traditional methods in multi-class settings.

Contribution

It introduces a novel approach combining Koopman operator theory with transformers for ECG classification, emphasizing the importance of dictionary selection for feature extraction.

Findings

Koopman features with tuned EDMD outperform wavelet features in four-class classification.

Wavelet features excel in binary classification tasks.

Hybrid Koopman-wavelet features do not improve accuracy over individual methods.

Abstract

Electrocardiogram (ECG) analysis is vital for detecting cardiac abnormalities, yet robust automated classification is challenging due to the complexity and variability of physiological signals. In this work, we investigate transformer-based ECG classification using features derived from the Koopman operator and wavelet transforms. Two tasks are studied: (1) binary classification (Normal vs. Non-normal), and (2) four-class classification (Normal, Atrial Fibrillation, Ventricular Arrhythmia, Block). We use Extended Dynamic Mode Decomposition (EDMD) to approximate the Koopman operator. Our results show that wavelet features excel in binary classification, while Koopman features, when paired with transformers, achieve superior performance in the four-class setting. A simple hybrid of Koopman and wavelet features does not improve accuracy. However, selecting an appropriate EDMD dictionary -- specifically a radial basis function dictionary with tuned parameters -- yields significant gains, surpassing the wavelet-only baseline and the hybrid wavelet-Koopman system. We also present a Koopman-based reconstruction analysis for interpretable insights into the learned dynamics and compare against a recurrent neural network baseline. Overall, our findings demonstrate the effectiveness of Koopman-based feature learning with transformers and highlight promising directions for integrating dynamical systems theory into time-series classification.