How to perform Weighted dimensionality reduction with Umap

Question

The title pretty much says it all, I have a df with 40+ dimension which I'd like to process into the Umap algorithm in order to have a 2-d output.

I would like to know if it is possible to weight the input columns differently for the purpose of studying the possible different Umap outcomes.

Thank you for your time

P.S. I work in python

Answer 1

Why not simply applying UMAP to A:

A = X*W

where X is your Nx40 matrix and W=diag(w) is a 40x40 diagonal matrix of weights w=[w1, w2,..., w40]?

Consider using normalized weights wi, i=1,2,...,40 such that sum(w) == 1, to distribute normally your information.