Representation Stability in High-Dimensional Noisy Time Series via Koopman-Based Features

Learning robust representations from high-dimensional noisy physiological time series remains challenging under patient variability, class imbalance, and signal perturbation. In this work, we investigate Koopman operator theory and Extended Dynamic Mode Decomposition (EDMD) as structured spectral representations for ECG time-series learning under patient-wise PTB-XL classification. Rather than proposing a new state-of-the-art classifier, we perform a systematic analysis of Koopman-only, deep neural, and hybrid spectral--deep representations, focusing on predictive performance, robustness, interpretability, and representation stability. Deep neural models achieve the strongest predictive accuracy, while hybrid spectral--deep representations slightly improve Macro-F1, suggesting that Koopman spectral descriptors provide complementary information for class-balanced learning. Although Koopman-only representations remain weaker in predictive performance, they capture meaningful temporal structure through compact and interpretable spectral descriptors. Robustness experiments further reveal that recomputed EDMD-based spectral representations become unstable under noisy perturbation, producing substantial eigenspectrum drift and degradation of hybrid representations. These findings highlight an important limitation of fixed spectral feature extraction in high-dimensional physiological settings. Overall, our results suggest that Koopman-inspired spectral representations are most useful as complementary analytical tools for studying temporal organization, robustness, and interpretability rather than as direct replacements for deep neural representations in physiological time-series learning.