Correlation clustering with stochastic labellings

Correlation clustering is the problem of finding a crisp partition of the vertices of a correlation graph in such a way as to minimize the disagreements in the cluster assignments. In this paper, we discuss a relaxation to the original problem setting which allows probabilistic assignments of vertices to labels. By so doing, overlapping clusters can be captured. We also show that a known optimization heuristic can be applied to the problem formulation, but with the automatic selection of the number of classes. Additionally, we propose a simple way of building an ensemble of agreement functions sampled from a reproducing kernel Hilbert space, which allows to apply correlation clustering without the empirical estimation of pairwise correlation values.