regression on Manifold using Kernel Dimension Reduction

An Algorithm for finding a new linear map for dimension reduction.

Introduction

This paper <ref>[1] Jen Nilsson, Fei Sha, Michael I. Jordan, Regression on Manifold using Kernel Dimension Reduction, 2007 - cs.utah.edu </ref>introduces a new algorithm for for discovering a manifold that best preserves the information relevant to a non-linear regression. The approach introduced by the authors involves combining the machinery of Kernel Dimesnion Reduction (KDR) with Laplacian Eigenmaps by optimizing the cross-covariance operators in kernel feature space.