I have $N$ points in a $D$-dimensional Poincare disk model. Ideally, I would like to have a centroid which would be representative of the cluster. To my knowledge, simple centroid calculation doesn't work in hyperbolic spaces as it does in Euclidean spaces.
So, my question is:
Is there a formula which given $N$ points computes their centroid?
If not, is there a closed-form solution for this problem when $N = 2$?
Thanks!
The $N=2$ hyperboloid formula Moishe shared generalizes, at least in the case of $D=2$. Check the answer to the following question for $N=3$ to see.
Centroid of a Triangle in The Poincare Disk
I haven't convinced myself the formula also works for higher dimensions.
You can easily move between the hyperboloid and ball models via stereographic projection.
(sorry, don't yet have enough reputation to just comment)