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