平面圈覆盖图
Planar Cycle Covering Graphs
摘要：
本文给出了平面二元马尔可夫随机场（MRF）最小能量位形的一个新的变分下界。我们的方法是基于添加辅助节点的平面嵌入图的每一个面，以捕捉一元潜力的影响。基态得到的近似可以有效地计算减少到最小重量的完美匹配。我们表明，变分参数的优化达到了相同的下界双重分解成原始图的所有周期的集合。我们证明了我们的变分优化收敛速度快，并提供高质量的解决方案，以硬组合问题的速度比竞争算法，优化相同的界限10- 100倍。
英文摘要：
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.
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