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# Analysis and Optimization of Graph Decompositions by Lifted Multicuts

*Proceedings of the 34th International Conference on Machine Learning*, PMLR 70:1539-1548, 2017.

#### Abstract

We study the set of all decompositions (clusterings) of a graph through its characterization as a set of lifted multicuts. This leads us to practically relevant insights related to the definition of classes of decompositions by must-join and must-cut constraints and related to the comparison of clusterings by metrics. To find optimal decompositions defined by minimum cost lifted multicuts, we establish some properties of some facets of lifted multicut polytopes, define efficient separation procedures and apply these in a branch-and-cut algorithm.