Planar Cycle Covering Graphs
We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture the effect of unary potentials. A ground state of the resulting approximation can be computed efficiently by reduction to minimum-weight perfect matching. We show that optimization of variational parameters achieves the same lower-bound as dual-decomposition into the set of all cycles of the original graph. We demonstrate that our variational optimization converges quickly and provides high-quality solutions to hard combinatorial problems 10-100x faster than competing algorithms that optimize the same bound.
Text ReferenceJulian Yarkony, Alex Ihler, and Charless Fowlkes. Planar cycle covering graphs. In UAI. 2011.
AUTHOR = "Yarkony, Julian and Ihler, Alex and Fowlkes, Charless",
TITLE = "Planar Cycle Covering Graphs",
BOOKTITLE = "UAI",
YEAR = "2011",
TAG = "grouping"