# Bi-clustering for time-varying relational count data analysis

## TL;DR

This paper introduces two novel bi-clustering models, dPIRM and a zero-inflated extension, for analyzing time-varying relational count data, effectively capturing latent structures and temporal dynamics.

## Contribution

The paper proposes two new models for bi-clustering relational count data over time, including a zero-inflated extension for sparse data, with detailed derivations and analysis.

## Key findings

- Both models effectively capture temporal dynamics in relational data.
- Simulation and real data demonstrate the models' effectiveness.
- Zero-inflated model handles sparse, short-interval data better.

## Abstract

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.