Curvature-Aware PCA with Geodesic Tangent Space Aggregation for Semi-Supervised Learning

ArXi:2604.18816v1 Announce Type: cross Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data ed 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.