I am studying linear and nonlinear motions of atoms. Regarding to the linear motion,I have used PCA to find PC of the highest variance and project it on the original data, so I can see only the motion of the highest amplitude. As you know PCA can handle only the linear variances. The projection with PCA is easy.
I need to do the same steps to find the nonlinear motions. I decided to use isomap as it has the ability to handle nonlinear motions. However, the problem is that: after dimension reduction with isomap I do not know how to reconstruct the higher dimensional data using the first dimension produced by isomap. Do you know any algorithm to solve this problem?