While there is an immense literature on Bayesian methods for clustering, the multiview case has received little attention. This problem focuses on obtaining distinct but statistically dependent clusterings in a common set of entities for different data types. For example, clustering patients into subgroups with subgroup membership varying according to the domain of the patient variables. A challenge is how to model the across-view dependence between the partitions of patients into subgroups. The complexities of the partition space make standard methods to model dependence, such as correlation, infeasible. In this article, we propose CLustering with Independence Centering (CLIC), a clustering prior that uses a single parameter to explicitly model dependence between clusterings across views. CLIC is induced by the product centered Dirichlet process (PCDP), a novel hierarchical prior that bridges between independent and equivalent partitions. We show appealing theoretic properties, provide a finite approximation and prove its accuracy, present a marginal Gibbs sampler for posterior computation, and derive closed form expressions for the marginal and joint partition distributions for the CLIC model. On synthetic data and in an application to epidemiology, CLIC accurately characterizes view-specific partitions while providing inference on the dependence level.

翻译：尽管贝叶斯聚类方法已有大量文献，但多视图情况受到的关注较少。该问题关注于在共同实体集合中，针对不同数据类型获得不同但统计上相互依赖的聚类结果。例如，根据患者变量的领域将患者分为不同的亚组，且亚组成员关系随领域变化。一个挑战是如何建模患者亚组划分在跨视图间的依赖关系。划分空间的复杂性使得相关等标准依赖建模方法不可行。本文提出聚类独立中心化（CLIC），这是一种聚类先验，通过单一参数显式建模跨视图聚类之间的依赖关系。CLIC由联合中心狄利克雷过程（PCDP）推导而来，这是一种新颖的分层先验，它连接了独立划分与等价划分。我们展示了吸引人的理论性质，提供了有限近似并证明了其准确性，提出了用于后验计算的边缘吉布斯采样器，并推导了CLIC模型边缘与联合划分分布的闭式表达式。在合成数据及流行病学应用中，CLIC准确刻画了视图特定划分，同时提供了对依赖水平的推断。