When I commented that that there may be non-euclidean equivalents to certain stat functions (average, mean, mode, etc), apparently there were others out there with the same general idea.

Some guys over at stanford are exploring hyperbolic spaces for machine learning, which is exactly the sort of applications I had in mind.

Very fascinating work, go check it out if it's something that interests you..
https://dawn.cs.stanford.edu/2019/...

And the related paper that it is based on:
http://proceedings.mlr.press/v80/...