Differentially Constrained Manifolds for Data-Efficient ECG Classification

Electrocardiogram (ECG) classification and automated arrhythmia detection for cardiac diagnosis are often limited by label scarcity, class imbalance, and strong inter patient variability, making data efficient machine learning a practical necessity. This paper studies a three class heartbeat classification setting using the MIT BIH Arrhythmia Database and develops a pipeline that combines geometry guided data augmentation, constraint guided perturbations, and deterministic subset selection for ECG signal analysis. The central mechanism treats local signal structure through discrete second differences and a curvature dependent inverse stiffness term called gravity, producing realistic parabolic jump augmentations that naturally stabilize training. In parallel, a learned class specific expression defines an implicit manifold constraint, enabling supervised scoring by margin drop under constraint respecting perturbations and unsupervised diversity selection through farthest point sampling in feature space. Together, these components form a unified methodology for improving generalization in small dataset ECG classification when training budgets are limited, while remaining reproducible under fixed random seeds. The method gives 89.3% accuracy for diverse weighted sample of small data regimes with budget size 900.