Good-enough Feature Representations with Persistent Homology in Physiological Systems

​​​Persistent Homology (PH) is a robust method in computational topology for data compression and feature extraction. However, its potential applications in analyzing physiological time series, which are often characterized by non-stationarity and non-linearity, remain largely unexplored. By addressing the challenges posed by the inherent variability and complexity of physiological signals, PH may offer novel insights into dynamic target patterns and improve predictive modeling in both clinical and non-clinical settings. In this study, we explore the application of PH to one-dimensional time series within physiological systems, focusing on the transferability of extracted features and their predictive performance in task classification. Our experiments demonstrate that PH can effectively capture essential multi-scale topological structures inherent to physiological signals using a low-dimensional representation that is more efficient than traditional methods such as Principal Component Analysis (PCA) and Discrete Fourier Transform (DFT). Additionally, utilizing the reduced representation constructed by PH, we find that the predictive accuracy of these models is comparable to, and in some cases, even superior to, those trained in the original high-dimensional space. Furthermore, we investigate the separation of primary (i.e., large-scale) topological structures from residual (i.e., small-scale) components, providing insights into interpreting these structures. Finally, we developed synthetic data augmentation techniques that leverage these topological structures to further enhance model robustness. These findings highlight that the topological-based feature extraction not only improves predictive performance but also minimizes data storage needs for model training, thus enabling more efficient data analysis in physiological research.