Electrocardiogram Classification with Transformers Using Koopman and Wavelet Features
Organizations: Interdisciplinary Center for Scientific Computing, Heidelberg University, Germany · Department of Mathematics and Computer Science, Heidelberg University, Heidelberg, Germany · Department of Theoretical Neuroscience, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany
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.
Figures & tables
| Method | Binary Cl F1 | 4-Class Cl F1 |
| Wavelet + Transformer | 0.750 0.02 | 0.700 0.03 |
| Koopman + Transformer | 0.697 0.01 | 0.771 0.02 |
| Hybrid (Wavelet + Koopman) + Transformer | 0.677 0.01 | 0.533 0.02 |
| Koopman + Transformer (After ablation) | 0.786 0.01 | 0.764 0.02 |
| RNN (Raw ECG, baseline) | 0.782 0.01 | 0.700 0.02 |
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
| Parameter | Short Form |
| Sampling Frequency | fs |
| Delay Embeddings | delay |
| Polynomial Degree | poly_deg |
| Number of RBF Centers | rbf_centers |
| RBF Kernel Bandwidth | rbf_sigma |
| SVD Rank Truncation | svd_rank |
| Component | Values |
| Koopman | fs = 125, delay = 8, poly_deg = 2, |
| rbf_centers = 0, rbf_sigma = 0.3, | |
| svd_rank = 16, ridge_reg = 1e-4, top_k = 8, | |
| window_sec = 2.0, stride_sec = 1.0 | |
| Transformer | layers = 4, heads = 8, emb_dim = 128, |
| ff_dim = 256, dropout = 0.1, |
Electrocardiogram Classification
Electrocardiogram classification uses machine learning to identify heart rhythms and cardiac conditions from ECG waveforms for screening, diagnosis, and monitoring.
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