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I have two spaces (not necessarily equal in dimension) with N points.
I am trying to find a bijection (pairing) of the points, such that the distances are preserved as well as possible.
I can’t seem to find a discussion of possible solutions or algorithms to this question online. Can anyone suggest keywords that I could search for? Does this problem have a name, or does it come up in any domain?
I believe you are looking for a Multidimensional Scaling algorithm where you are minimizing the total change in distance. Unfortunately, I have very little experience in this area and can’t be of much more help.