Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning
Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model nonlinearity but often sacrifice the spectral structure and stability of PCA. We propose \emph{Geodesic Tangent Space Aggregation PCA (GTSA-PCA)}, a geometric extension of PCA that integrates curvature awareness and geodesic consistency within a unified spectral framework. Our approach replaces the global covariance operator with curvature-weighted local covariance operators defined over a $k$-nearest neighbor graph, yielding local tangent subspaces that ada...
| Authors | Alexandre L. M. Levada |
|---|---|
| Primary category | cs.LG |
| Published | 20 April 2026 |
| Last updated at source | 20 April 2026 |
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