Recent approaches to non-linear dimensionality reduction.

I am learning about non-linear dimensionality reduction (so far only older stuff like isomap and LLE). And I had a few questions:

1. Most implemented packages for isomap that I found (in R) simply mapped all my data to the manifold they "found". Is there a way to get the map itself (function mapping from input space to the manifold)? So that I would be able to learn the manifold on the training set and apply it to test sets?

2. What are the newer/better methods for non-linear dimensionality reduction?

3. How does non-linear reduction perform for small sample sizes (p >> n)?

Thanks a lot, PMW.