最小割聚类的信息论推导
An information-theoretic derivation of min-cut based clustering
摘要：
最小割聚类，基于最小化的两个启发式成本函数之一提出的Shi和Malik，已经产生了巨大的研究，分析和算法，在图分割和图像分割社区在过去的十年。然而，目前还不清楚，这些理论是否可以从一个更普遍的原则，促进推广到新的问题设置。出于现有的图划分框架，我们得到优化的相关信息之间的关系，定义在信息瓶颈方法，和正则化的K-分区图的切割。对于快速混合图，我们表明，由施和马利克引入的成本函数可以很好地近似为损失率的预测信息的位置上的图的随机游走。对于从随机算法设计的社区结构模型生成的图，最佳信息理论划分和最佳最小割划分是相同的高概率。
英文摘要：
Min-cut clustering, based on minimizing one of two heuristic cost-functions proposed by Shi and Malik, has spawned tremendous research, both analytic and algorithmic, in the graph partitioning and image segmentation communities over the last decade. It is however unclear if these heuristics can be derived from a more general principle facilitating generalization to new problem settings. Motivated by an existing graph partitioning framework, we derive relationships between optimizing relevance information, as defined in the Information Bottleneck method, and the regularized cut in a K-partitioned graph. For fast mixing graphs, we show that the cost functions introduced by Shi and Malik can be well approximated as the rate of loss of predictive information about the location of random walkers on the graph. For graphs generated from a stochastic algorithm designed to model community structure, the optimal information theoretic partition and the optimal min-cut partition are shown to be the same with high probability.
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