When clustering high-dimensional data, it is often important to identify variables that discriminate the clusters. Meanwhile, a common issue in clustering is to determine the number of clusters. In this study, we propose a new method that simultaneously performs clustering and variable selection, while inferring the number of clusters from the data. We formulate the clustering problem using a finite mixture model with a symmetric Dirichlet weights prior, while also placing a prior on the number of components. That is, we utilize a mixture of finite mixtures. We handle the variable selection problem by introducing a latent binary vector, which represents the inclusion/exclusion of variables. We update the binary vector for variable selection using a Metropolis algorithm and perform inference on the cluster structure using a split–merge Markov chain Monte Carlo technique. We demonstrate the advantage of our method using simulated and two real DNA microarray datasets.

在对高维数据进行聚类时，识别区分聚类的变量通常很重要。同时，聚类中的一个常见问题是确定聚类的数量。在这项研究中，我们提出了一种同时执行聚类和变量选择的新方法，同时从数据中推断出聚类的数量。我们使用具有对称 Dirichlet 权重先验的有限混合模型来制定聚类问题，同时还对组件数量进行了先验。也就是说，我们使用有限混合的混合。我们通过引入一个潜在的二元向量来处理变量选择问题，它表示变量的包含/排除。我们使用 Metropolis 算法更新变量选择的二元向量，并使用分裂合并马尔可夫链蒙特卡罗技术对集群结构进行推理。我们使用模拟的和两个真实的 DNA 微阵列数据集证明了我们的方法的优势。