ABSTRACT The use of a finite mixture of normal distributions in model-based clustering allows us to capture non-Gaussian data clusters. However, identifying the clusters from the normal components is challenging and in general either achieved by imposing constraints on the model or by using post-processing procedures. Within the Bayesian framework, we propose a different approach based on sparse finite mixtures to achieve identifiability. We specify a hierarchical prior, where the hyperparameters are carefully selected such that they are reflective of the cluster structure aimed at. In addition, this prior allows us to estimate the model using standard MCMC sampling methods. In combination with a post-processing approach which resolves the label switching issue and results in an identified model, our approach allows us to simultaneously (1) determine the number of clusters, (2) flexibly approximate the cluster distributions in a semiparametric way using finite mixtures of normals and (3) identify cluster-specific parameters and classify observations. The proposed approach is illustrated in two simulation studies and on benchmark datasets. Supplementary materials for this article are available online.

中文翻译：

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使用贝叶斯估计识别混合物的混合物

摘要 在基于模型的聚类中使用正态分布的有限混合使我们能够捕获非高斯数据聚类。然而，从正常组件中识别集群是具有挑战性的，通常可以通过对模型施加约束或使用后处理程序来实现。在贝叶斯框架内，我们提出了一种基于稀疏有限混合的不同方法来实现可识别性。我们指定了一个分层先验，其中超参数是经过精心选择的，以便它们反映所针对的集群结构。此外，此先验允许我们使用标准 MCMC 采样方法来估计模型。结合可解决标签切换问题并生成已识别模型的后处理方法，我们的方法允许我们同时 (1) 确定集群的数量，(2) 使用有限的法线混合以半参数方式灵活地近似集群分布，以及 (3) 识别特定于集群的参数并对观察进行分类。所提出的方法在两个模拟研究和基准数据集上进行了说明。本文的补充材料可在线获取。