Abstract:
In this talk I consider point clouds obtained as samples of a ground-truth
measure. The purpose is to investigate approaches to clustering based on
minimizing objective functionals defined on proximity graphs of the given sample of
points. The focus is on functionals based on graph cuts like the Cheeger and ratio cuts.
I will discuss some results about the convergence of minimizers of these
cuts as the sample size increases, towards a minimizer of a corresponding continuum cut (which
partitions the ground-truth measure). Moreover, I will present sharp conditions
on how the connectivity radius can be scaled with respect to the number of
sample points for the consistency to hold. I will provide results for
two-way and for multiway cuts. This is joint work with Dejan Slepcev, James von Brecht, Thomas Laurent and Xavier Bresson. |