  We propose a graph clustering formulation based on multicut (a.k.a. weighted
correlation clustering) on the complete graph. Our formulation does not need
specification of the graph topology as in the original sparse formulation of
multicut, making our approach simpler and potentially better performing. In
contrast to unweighted correlation clustering we allow for a more expressive
weighted cost structure. In dense multicut, the clustering objective is given
in a factorized form as inner products of node feature vectors. This allows for
an efficient formulation and inference in contrast to multicut/weighted
correlation clustering, which has at least quadratic representation and
computation complexity when working on the complete graph. We show how to
rewrite classical greedy algorithms for multicut in our dense setting and how
to modify them for greater efficiency and solution quality. In particular, our
algorithms scale to graphs with tens of thousands of nodes. Empirical evidence
on instance segmentation on Cityscapes and clustering of ImageNet datasets
shows the merits of our approach.
