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

Learning robust representations from physiological time series remains challenging under patient variability, class imbalance, and signal perturbation. We investigate Koopman operator theory and EDMD as structured dynamical representations for studying representation geometry, robustness, and stability in high-dimensional physiological time series. Using patient-wise PTB-XL classification as a controlled testbed, we compare Koopman-only, deep neural, and hybrid spectral--deep representations. Our analysis reveals a stability--performance tradeoff. Deep neural models achieve the strongest predictive accuracy, whereas hybrid spectral--deep representations slightly improve Macro-F1, indicating that Koopman spectral descriptors provide complementary information for class-balanced learning. Although less competitive in predictive performance, Koopman representations capture temporal structure through compact spectral descriptors. Robustness experiments show that recomputed EDMD-based representations become unstable under perturbation, producing eigenspectrum drift and degradation of hybrid representations. These results highlight limitations of fixed spectral feature extraction and suggest that Koopman-inspired representations are most useful as complementary tools for studying temporal organization, robustness, interpretability, and representation geometry rather than as direct replacements for deep neural representations.