Abstract Relational count data are often obtained from sources such as simultaneous purchase in online shops and social networking service information. Clustering such relational count data reveals the latent structure of the relationship between objects such as household items or people. When relational count data observed at multiple time points are available, it is worthwhile incorporating the time structure into the clustering result to understand how objects move between the clusters over time. In this paper, we propose two clustering methods for analyzing time-varying relational count data. The first model, the dynamic Poisson infinite relational model (dPIRM), handles time-varying relational count data. In the second model, which we call the dynamic zero-inflated Poisson infinite relational model, we further extend the dPIRM so that it can handle zero-inflated data. Proposing both two models is important as zero-inflated data are often encountered, especially when the time intervals are short. In addition, by explicitly deriving the relevant full conditional distributions, we describe the features of the estimated parameters and, in turn, the relationship between the two models. We show the effectiveness of both models through a simulation study and a real data example.

中文翻译：

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时变关系计数数据的聚类

摘要 关系计数数据通常来自在线商店的同时购买和社交网络服务信息等来源。对这种关系计数数据进行聚类揭示了诸如家居用品或人之类的对象之间关系的潜在结构。当在多个时间点观察到的关系计数数据可用时，将时间结构纳入聚类结果以了解对象如何随时间在聚类之间移动是值得的。在本文中，我们提出了两种用于分析时变关系计数数据的聚类方法。第一个模型，动态泊松无限关系模型 (dPIRM)，处理随时间变化的关系计数数据。在第二个模型中，我们称之为动态零膨胀泊松无限关系模型，我们进一步扩展了 dPIRM，使其可以处理零膨胀数据。提出这两种模型很重要，因为经常会遇到零膨胀数据，尤其是在时间间隔很短的情况下。此外，通过显式导出相关的全条件分布，我们描述了估计参数的特征，进而描述了两个模型之间的关系。我们通过模拟研究和真实数据示例展示了两种模型的有效性。