Multicuts and Perturb & MAP for Probabilistic Graph Clustering

TL;DR

This paper introduces a probabilistic graphical model approach for graph clustering that improves the accuracy and efficiency of sampling and marginal estimation, applicable to image segmentation and social network analysis.

Contribution

It combines recent advances in MAP inference and perturbation methods to enhance probabilistic graph clustering with a mathematically grounded framework.

Findings

More accurate marginal distribution estimation

Efficient sampling of clusterings

Applicable to various graph-based problems

Abstract

We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to rectify local data term cues so as to close contours and to obtain valid partitions. We exploit recent progress on globally optimal MAP inference by integer programming and on perturbation-based approximations of the log-partition function, in order to sample clusterings and to estimate marginal distributions of node-pairs both more accurately and more efficiently than state-of-the-art methods. Our approach works for any graphically represented problem instance. This is demonstrated for image segmentation and social network cluster analysis. Our mathematical ansatz should be relevant also for other combinatorial problems.