ManifoldLearning

[mateuszbaran]

There is a package ManifoldLearning: https://github.com/wildart/ManifoldLearning.jl . Only partially related but we may still want to take a look at what it does.

[kellertuer]

They try to estimate the low dimensional manifold the data (from some high-dimensional vector space) lies on and provide properties of that; so the setting is different.

[mateuszbaran]

Yes but we could have a similar thing just for high-dimensional manifolds. Would that be manifold manifold learning? 🙂 For example laplacian eigenmaps could be easily adapted, probably some other too, by replacing metric in the kNN step.

[kellertuer]

That would then be Laplace Beltrami eigenmaps? I just have no experience in this direction.

[mateuszbaran]

There seems to be a lot of slightly different variations on the same idea. Do you have a reference for Laplace Beltrami eigenmaps? I only have the basic idea of how such embeddings work.

[kellertuer]

No, I am not aware of a (good) reference, because I haven't worked much with Laplace Beltrami per se.