A semi-supervised framework for mapping data to the intrinsic manifold

This paper presents a novel scheme for manifold learning. Different from the previous work reducing data to Euclidean space which cannot handle the looped manifold well, we map the scattered data to its intrinsic parameter manifold by semi-supervised learning. Given a set Of partially labeled points, the map to a specified parameter manifold is computed by an iterative neighborhood average method called Anchor Points Diffusion procedure (APD). We explore this idea on the most frequently used closeformed manifolds, Stiefel manifolds whose special cases include hyper sphere and orthogonal group. The experiments show that APD can recover the underlying intrinsic parameters of points on scattered data manifold successfully.