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We present a probabilistic graphical model formulation for the graphclustering problem. This enables to locally represent uncertainty of imagepartitions by approximate marginal distributions in a mathematicallysubstantiated way, and to rectify local data term cues so as to close contoursand to obtain valid partitions.  We exploit recent progress on globally optimal MAP inference by integerprogramming and on perturbation-based approximations of the log-partitionfunction, in order to sample clusterings and to estimate marginal distributionsof node-pairs both more accurately and more efficiently than state-of-the-artmethods. Our approach works for any graphically represented problem instance.This is demonstrated for image segmentation and social network clusteranalysis. Our mathematical ansatz should be relevant also for othercombinatorial problems.

Multicuts and Perturb & MAP for Probabilistic Graph Clustering