Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

2026-03-09

AI Summary

This study addresses the challenge of automatic electrocardiogram (ECG) classification arising from signal complexity and variability by proposing a novel approach that integrates dynamical systems theory with temporal modeling. The method leverages extended dynamic mode decomposition (EDMD) to approximate the Koopman operator, combined with wavelet transform for feature extraction, and—uniquely—integrates Koopman-based features into a Transformer architecture for both binary (normal/abnormal) and four-class (normal, atrial fibrillation, ventricular arrhythmia, conduction block) ECG classification tasks. A tunable radial basis function dictionary is innovatively introduced to enhance performance, while Koopman-based signal reconstruction improves model interpretability. Experimental results demonstrate that, under specific EDMD configurations, the proposed method significantly outperforms baselines using wavelet features, hybrid approaches, and recurrent neural networks, thereby validating the efficacy of dynamical systems–derived features in ECG classification.

Technology Category

• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Electrocardiogram classification
• Koopman operator
• Wavelet features
• Transformer
• Time-series classification

Innovation

• Koopman operator
• Transformers
• Wavelet features
• EDMD
• ECG classification