Local Distance Preservation in the GP-LVM through Back Constraints

by Neil Lawrence and Joaquin Quinonero-Candela

This is a piece of work following GP-LVM. The idea is so simple that I suddenly found out I was cheated in a way. It is not a very elusive idea: the GP-LVM model maximizes the likelihood function by solving a non-linear optimization. The solution is the coordinates in the low-dimensional space. Now in order to impose our ``local information'' in the high dimensional space, it is very natural that we assume there exist a mapping (parametric or non-parametric) such that the low dimensional coordinates are represented by the image of high-dimensional coordinates.

Then we solve the constrained version of maximization of the likelihood.

I think the application of GP-LVM is more attractive than this paper -,-b