An important task in the analysis of graphs is separating nodes into densely connected groups with little interaction between each other. Prominent methods here include flow based graph cutting procedures as well as statistical network modeling approaches. However, adequately accounting for this, the so-called community structure, in complex networks remains a major challenge. We present a novel generic Bayesian probabilistic model for graph cutting in which we derive an analytical solution to the marginalization of nuisance parameters under constraints enforcing community structure. As a part of the solution a large scale approximation for integrals involving multiple incomplete gamma functions is derived. Our multiple cluster solution presents a generic tool for Bayesian inference on Poisson weighted graphs across different domains. Applied on three real world social networks as well as three image segmentation problems our approach shows on par or better performance to existing spectral graph cutting and community detection methods, while learning the underlying parameter space. The developed procedure provides a principled statistical framework for graph cutting and the Bayesian Cut source code provided enables easy adoption of the procedure as an alternative to existing graph cutting methods.

中文翻译：

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贝叶斯切割

图分析中的一项重要任务是将节点分成紧密连接的组，彼此之间几乎没有交互。这里的主要方法包括基于流的图形切割程序以及统计网络建模方法。然而，在复杂网络中充分考虑这一点，即所谓的社区结构仍然是一个重大挑战。我们提出了一种用于图形切割的新型通用贝叶斯概率模型，在该模型中，我们推导出了在强制执行社区结构的约束下对有害参数边缘化的解析解。作为解决方案的一部分，推导出涉及多个不完整伽马函数的积分的大规模近似。我们的多集群解决方案为跨不同域的泊松加权图提供了贝叶斯推理的通用工具。应用于三个现实世界的社交网络以及三个图像分割问题，我们的方法在学习基础参数空间的同时，表现出与现有谱图切割和社区检测方法相当或更好的性能。开发的程序为图形切割提供了一个有原则的统计框架，所提供的贝叶斯切割源代码可以轻松采用该程序作为现有图形切割方法的替代方案。