I have $N$ points in $D$ dimensions, were $D$ is big, for sure more than $100$. $N$ is also big.
The goal is to produce an algorithm in my code, that will take as input this dataset and will give another one (in a different matrix), that will be randomly rotated.
I have used Euler rotation, but the time complexity of it is $O(N\cdot D\cdot D)$.
Chanop and Hartley note in their paper "Optimised KD-trees for fast image descriptor matching", that:
but searching the internet didn't help me much, so I literally don't know how to perform this task. I am not asking for code, but for guidance, for what I should do to achieve my goal.
A relevant -maybe- question is this in this site.