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.



How to compute the entropy of a random variable with values in a metric space?
1. Estimate the probability density, using [Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation)
2. Compute the differential entropy.


