I think you would prefer something like a support vector machine over k-nn for better learned point-wise local rescaling (you could also use eg ISOMAP or MDS to

I think you would prefer something like a support vector machine over k-nn for better learned point-wise local rescaling (you could also use eg ISOMAP or MDS to try to linearize the manifold), which you could also use w various tda methods (see the giotto-tda github repo jupyter notebooks for some similar examples)