  We consider the problem of learning a set from random samples. We show how
relevant geometric and topological properties of a set can be studied
analytically using concepts from the theory of reproducing kernel Hilbert
spaces. A new kind of reproducing kernel, that we call separating kernel, plays
a crucial role in our study and is analyzed in detail. We prove a new analytic
characterization of the support of a distribution, that naturally leads to a
family of provably consistent regularized learning algorithms and we discuss
the stability of these methods with respect to random sampling. Numerical
experiments show that the approach is competitive, and often better, than other
state of the art techniques.
