Consider a set of points $\Omega \subset \mathbb{R}^n$ (to make it simple, consider $n=2$). So you basically have a bunch of points on a plane.
I need to find good metrics that can describe the closeness, clustering of this dispersion of points. Scalar quantities is what I am looking for, in order to answer these questions:
- Are the points forming a single compact mass?
- Are the points quite uniformly distributed across the plane?
- Are the points generating some clusters?
- If so, are they arranged in many clusters? Few clusters?