时变关系计数数据的双聚类分析
Bi-clustering for time-varying relational count data analysis
摘要：
关系计数数据通常从在线商店中的同时购买和社交网络服务信息等来源获得。双聚类这样的关系计数数据揭示了对象之间的关系的潜在结构，如家庭物品或人。当在多个时间点观察到的关系计数数据可用时，值得将时间结构合并到双聚类结果中，以了解对象如何随时间在聚类之间移动。在本文中，我们提出了两个双聚类方法来分析时变关系计数数据。第一个模型，动态泊松无限关系模型（dPSTOM），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dPoisson，使其可以处理零膨胀数据。提出这两个模型是很重要的，因为零膨胀的数据经常遇到，特别是当时间间隔很短。此外，通过显式地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。我们通过仿真研究和实际数据的例子表明这两种模型的有效性。
英文摘要：
Relational count data are often obtained from sources such as simultaneous purchase in online shops and social networking service information. Bi-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 bi-clustering result to understand how objects move between the cluster over time. In this paper, we propose two bi-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.
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