Learning Topology with the Generative Gaussian Graph and the EM Algorithm

Given a set of points and a set of prototypes representing them, how to create a graph of the prototypes whose topology accounts for that of the points? This problem had not yet been explored in the framework of statistical learningtheory. In this work, we propose a generative model based on the Delaunay graph of the prototypes and the Expectation-Maximization algorithm to learn the parameters. This work is a first step towards the construction of a topological model of a set of points grounded on statistics.