I just went into the Diffusion algorithm behind the package, and realized that there is no guarantee that you can go from a vector in the diffusion space back into the data space.
This is because the diffusion space represent the distances to the original data points. So if at least two points are different, the null vector in the diffusion space (at distance 0 of all original data points in the data space) will have no equivalent in the data space.
Hope this can help someone else!
using pydiffmap, I could find a nice low dimension Manifold in my data, and extract what seems to be meaningful low dimension components.
I would like now to reverse the operator, and project my data back to my original high dimensional space keeping only these few important dimensions I could identify.
First, is this mathematically possible? And if so how to do it?
Thanks a lot!
pydiffmap: How to reverse Diffusion Map Embedding and reconstruct original variables from several principal components?