[Paper Review] Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features

Sucheta Ghosh, Zahra Monfared|arXiv (Cornell University)|Mar 9, 2026

ECG Monitoring and Analysis0 citations

TL;DR

The paper evaluates Koopman-based and wavelet features with Transformer classifiers for ECG; refined Koopman features with EDMD outperform wavelet baselines in multi-class tasks, while wavelets excel in binary tasks.

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.

Motivation & Objective

• Assess the effectiveness of Koopman-based features with Transformer classifiers for ECG classification.
• Compare Koopman features against wavelet-based features in binary and four-class ECG tasks.
• Investigate a hybrid of Koopman and wavelet features and refinement of EDMD parameters.
• Provide interpretability insights via Koopman-based reconstruction and eigenstructure analysis.

Proposed method

• Extract wavelet-based features via discrete wavelet transform for Transformer input.
• Approximate the Koopman operator using Extended Dynamic Mode Decomposition with an RBF dictionary to derive eigenvalues, eigenfunctions, and related features for Transformer input.
• Optionally concatenate Koopman and wavelet features and feed to a Transformer encoder (hybrid approach).
• Refine Koopman features by tuning EDMD hyperparameters (delay, rbf_centers, rbf_sigma, svd_rank) to improve performance.
• Train Transformer-based classifiers on features with fixed-length ECG windows and compare to an RNN baseline on MIMIC-IV-ECG data.
• Evaluate binary (Normal vs Non-normal) and four-class (Normal, AFib, Ventricular, Block) tasks; report F1 scores and reconstruction quality.

Experimental results

Research questions

• RQ1 Can Koopman-based features with Transformers achieve superior ECG classification performance compared to wavelet-based features?
• RQ2 Do hybrid wavelet and Koopman features improve performance over single-feature approaches?
• RQ3 How do EDMD hyperparameters affect Koopman-based Transformer performance on ECG data?
• RQ4 What does Koopman-based reconstruction reveal about learned cardiac dynamics and interpretability?

Key findings

• Wavelet+Transformer provides strong binary-class performance (F1 = 0.75).
• Koopman+Transformer outperforms in four-class classification (F1 = 0.771 before refinement; 0.764 after ablation in the table, but the ablation row shows 0.764 for 4-class).
• Koopman+Transformer after ablation achieves the best overall binary and four-class performance (F1 = 0.786 for binary; 0.764 for four-class).
• Hybrid Wavelet+Koopman + Transformer underperforms compared with single-feature systems (Binary F1 = 0.677; Four-class F1 = 0.533).
• RNN baseline (on raw ECG) yields competitive binary performance but is computationally more expensive; Koopman and wavelet feature methods scale more linearly and are more efficient.