Gaussian Process Manifold Kernel Dimensionality Reduction (GPMKDR) [1]

Constructing optimal regressors is an important task in computer vision. Problems such as tracking, 3D human and general object pose estimation, image and signal denoising, illumination direction estimation are but some of the problems that can be formulated in the regression setting. 
In this work we consider the task of discovering low-dimensional manifolds that preserve information relevant for a general nonlinear regression. We have proposed a novel dimension reduction approach called Gaussian Process Manifold Kernel Dimensional Reduction (GPMKDR), induced by reformulating the manifold kernel dimensional reduction (mKDR) in the Gaussian Process (GP) framework. In this framework, a closed-form solution for mKDR is given by the maximum eigenvalue-eigenvector solution to a kernelized problem. 

Sufficient Dimensionality Reduction (SDR)

Gaussian Process Manifold KDR

• [1] K. Moon and V. Pavlovic. “Visual inference using Gaussian process manifold kernel dimensionality reduction”. 2008.