Diffusion Map

[dynamic-queries]

For non-linear data reduction, Diffusion maps should be considered, as there is good deal of work done here wrt Data Driven MOR methods.

https://www.sciencedirect.com/science/article/pii/S1063520306000546?via%3Dihub

Implementation friendly description at https://mediatum.ub.tum.de/download/1356533/1356533.pdf , page 46

[dynamic-queries]

Could leverage implementations from https://github.com/wildart/ManifoldLearning.jl here.
Although I would like to build on it for optimal embedding as they discuss here https://www.sciencedirect.com/science/article/pii/S1063520315000949?ref=cra_js_challenge&fr=RR-1 .
@ChrisRackauckas Would it make sense re-implementing the diffusion maps to add this "optimal embedding feature" ?

[ChrisRackauckas]

Reusing code is usually good, though I know there are some issues with many of the diffusion map libraries in Julia so 🤷 . https://github.com/wildart/ManifoldLearning.jl has had maintenance issues since forever so reimplementing might be a fine idea.