Manifold-Constrained Data Augmentation via SPD Geometry for Self-Supervised ECG Representation Learning
Keywords:
Self-Supervised Learning, Electrocardiogram (ECG), Riemannian Manifold, Contrastive Learning, Physiological Data AugmentationAbstract
Self-supervised learning for electrocardiogram (ECG) analysis often relies on stochastic data augmentation techniques such as random cropping or noise injection. These conventional methods, however, may generate physiologically implausible signals that degrade downstream representation quality. We propose a novel data augmentation framework that operates on a low-dimensional Riemannian manifold of symmetric positive-definite matrices. The core idea is to embed each multi-lead ECG segment as a point on this manifold, thereby capturing inter-lead correlations in a geometry-constrained manner. Our method first partitions the ECG signal into temporal patches and computes sample covariance matrices for each patch. These matrices are then projected into a lower-dimensional space via a learnable linear map, preserving the essential lead-correlation structure. A transformer encoder processes the resulting sequence of tangent-space vectors, and the output is aggregated to produce a canonical manifold representation of the entire segment. To enforce physiological validity, we introduce a physics-informed residual block that corrects the embedded point toward a prior derived from Einthoven’s triangle constraints. Augmented views are subsequently generated through geodesic interpolation between the corrected point and a randomly sampled neighbor on the manifold, followed by a harmonic perturbation of the eigenvalues. This procedure yields smooth variations in the covariance structure while maintaining the eigenbasis, thereby mimicking natural physiological variability. The augmented covariance matrix is then projected back to the original lead space, and a Gaussian process is sampled to reconstruct the ECG time series. The entire pipeline is trained end-to-end with a contrastive objective. Our approach ensures that all synthesized signals remain within the submanifold of physiologically plausible covariance structures, a critical advantage over stochastic augmentation methods. We demonstrate that this manifold-constrained augmentation significantly improves the quality of learned ECG representations for downstream tasks such as arrhythmia classification and patient identification.
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