Hypersurface fitting via Jacobian nonlinear PCA on Riemannian space

Abstract

The subspace fitting method based on usual nonlinear principle component analysis (NLPCA), which minimizes the square distance in feature space, sometimes derives bad estimation because it does not reflect the metric on input space. To alleviate this problem, authors proposed the subspace fitting method based on NLPCA with considering the metric on input space, which is called Jacobian NLPCA. The proposed method is efficient when the metric of input space is defined. The proposed method can be rewritten as kernel method as explained in the paper. © 2011 Springer-Verlag.