Manifold Fitting by Successive Tangent-Space Projection
This study addresses the inherent trade-off between fitting accuracy and geometric coverage when recovering latent manifold structures from noisy observations. To this end, we propose a continuous tangent space projection algorithm that achieves high-precision manifold fitting by iteratively suppressing normal noise while preserving tangential variations. Theoretically, we define the fixed-point set of local neighborhoods, prove that its geometric localization order is O(σ²), and introduce a multiscale extension to eliminate curvature bias. Numerical experiments demonstrate that the proposed method significantly mitigates curvature shrinkage under high-noise conditions, outperforming existing approaches in both fitting accuracy and geometric coverage.