In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior samples for the latent allocation variables can be effectively obtained in a wide range of clustering models, including finite mixtures, infinite mixtures, hidden Markov models and block models for networks. However, due to the categorical nature of the clustering variables and the lack of scalable algorithms, summary tools that can interpret such samples are not available. We adopt a Bayesian decision theoretical approach to define an optimality criterion for clusterings and propose a fast and context-independent greedy algorithm to find the best allocations. One important facet of our approach is that the optimal number of groups is automatically selected, thereby solving the clustering and the model-choice problems at the same time. We consider several loss functions to compare partitions and show that our approach can accommodate a wide range of cases. Finally, we illustrate our approach on both artificial and real datasets for three different clustering models: Gaussian mixtures, stochastic block models and latent block models for networks.

中文翻译：

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潜在变量聚类模型的最佳贝叶斯估计量。

在聚类分析中，兴趣在于概率性地将个人，项目或观察结果划分为组，以使属于同一组的那些人共享相似的属性或关系配置文件。在广泛的聚类模型中，包括有限混合，无限混合，隐马尔可夫模型和网络块模型，可以有效地获得潜在分配变量的贝叶斯后验样本。但是，由于聚类变量的分类性质和缺乏可伸缩的算法，因此无法使用可解释此类样本的汇总工具。我们采用贝叶斯决策理论方法来定义聚类的最优准则，并提出一种快速且独立于上下文的贪心算法以找到最佳分配。我们方法的一个重要方面是，可以自动选择最佳的组数，从而同时解决聚类和模型选择问题。我们考虑了几个损失函数来比较分区，并表明我们的方法可以适应各种情况。最后，我们在三种不同的聚类模型的人工和真实数据集上说明了我们的方法：高斯混合，随机块模型和网络的潜在块模型。