  Sum-of-norms clustering is a convex optimization problem whose solution can
be used for the clustering of multivariate data. We propose and study a
localized version of this method, and show in particular that it can separate
arbitrarily close balls in the stochastic ball model. More precisely, we prove
a quantitative bound on the error incurred in the clustering of disjoint
connected sets. Our bound is expressed in terms of the number of datapoints and
the localization length of the functional.
