贝叶斯方法聚类真实值，分类和网络数据：通过变分方法的解决方案
Bayesian approach to clustering real value, categorical and network data: solution via variational methods
摘要：
数据聚类，包括寻找网络社区等问题，可以通过贝叶斯方法纳入系统框架。然而，将贝叶斯方法应用于实际问题可能相当具有挑战性。在大多数情况下，通过蒙特卡罗抽样或变分方法来探索解决方案。在这里，我们进一步研究变分方法在聚类问题中的应用。我们介绍了生成模型的基础上隐藏的组结构和先验分布。我们推广了Jaynes的先验分布，并基于对称性参数导出了先验分布。作为一个案例研究，我们解决的问题，双边聚类的实值数据和聚类数据表示的超图或二分图。从变分计算，并根据数据的起始统计模型，我们得到一个变分贝叶斯算法，一个广义版本的期望最大化算法与内置的惩罚模型的复杂性或偏见。我们证明了良好的性能的变分贝叶斯算法使用测试的例子。
英文摘要：
Data clustering, including problems such as finding network communities, can be put into a systematic framework by means of a Bayesian approach. The application of Bayesian approaches to real problems can be, however, quite challenging. In most cases the solution is explored via Monte Carlo sampling or variational methods. Here we work further on the application of variational methods to clustering problems. We introduce generative models based on a hidden group structure and prior distributions. We extend previous attends by Jaynes, and derive the prior distributions based on symmetry arguments. As a case study we address the problems of two-sides clustering real value data and clustering data represented by a hypergraph or bipartite graph. From the variational calculations, and depending on the starting statistical model for the data, we derive a variational Bayes algorithm, a generalized version of the expectation maximization algorithm with a built in penalization for model complexity or bias. We demonstrate the good performance of the variational Bayes algorithm using test examples.
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