How to predict new data after dimensionality reduction with Isomap and LLE?”

I have a data frame with 12 features and 39 individuals. I applied LLE, PCA and Isomap for feature reduction. I know how to get the loading matrix from PCA to predict a new data but i can t find a way to do the same thing with the other two approaches (LLE/Isomap).
I m using RDRToolbox

It is a lot more complicated using manifold methods (esp with nearest neighbors).

The dimRed package can compute both of those (and more) but I think that there is no LLE projection for new data

For IsoMap, there is a recipe step that can be used to produce features for new data.

Relatedly, the GH version of embed has a recipe step for UMAP that projects for new data (supervised and unsupervised).

One last thing... for this small sample size, you might want to stick to simple linear rotational methods like PCA. I would be worried about how well these nonlinear projections would generalize with 39 samples.

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