I have a cloud of points, and I want to compute its 'diversity'. Variance is not appropriate, because a cloud clustering around few points can still have a large variance.
To that end, I see the cloud of points as the realizations of a random variable.
I want to compute the topological entropy of a random variable, with values in a metric space $(X,d)$.
I only know $N$ (large) realisations of this variable, and I can compute the relative distances between them.