# COIN: Co-Cluster Infomax for Bipartite Graphs

**Authors:** Baoyu Jing, Yuchen Yan, Yada Zhu, Hanghang Tong  
**arXiv:** [2206.00006](https://arxiv.org/abs/2206.00006)  
**Date:** 2022-05-31  
**Summary page:** https://www.summarizepaper.com/en/paper/2206.00006v2/

## Key points

- Bipartite graphs are used in recommender systems, information retrieval, and drug discovery.
- Learning informative node embeddings is a fundamental challenge for bipartite graphs.
- Recent self-supervised learning methods discriminate instance-wise positive and negative node pairs that could contain cluster-level errors.
- A novel co-cluster infomax (COIN) framework is introduced to address this issue by maximizing the mutual information of co-clusters.
- COIN can easily calculate mutual information and is an end-to-end coclustering method that can be trained jointly with other objective functions and optimized via backpropagation.
- Theoretical analysis proves that COIN effectively increases the mutual information of node embeddings while being upperbounded by the prior distributions of nodes.
- COIN is extensively evaluated on various benchmark datasets and tasks to demonstrate its effectiveness.
- Sensitivity experiments show that COIN performs best when the number of clusters is around the ground truth number of classes and has small variances for different coefficients λ for mutual information on Wikipedia datasets.
- Overall, COIN provides a powerful solution to learning informative node embeddings in bipartite graphs by capturing cluster level information through maximizing mutual information of co-clusters.

## Summary

Bipartite graphs are widely used in various applications such as recommender systems, information retrieval and drug discovery. However, a fundamental challenge for bipartite graphs is how to learn informative node embeddings. Recent self-supervised learning methods have shown success in this area but their objectives discriminate instance-wise positive and negative node pairs that could contain cluster-level errors. To address this issue, a novel co-cluster infomax (COIN) framework is introduced in this paper. COIN captures the cluster-level information by maximizing the mutual information of co-clusters. Unlike previous infomax methods that estimate mutual information using neural networks, COIN can easily calculate mutual information. Additionally, COIN is an end-to-end coclustering method that can be trained jointly with other objective functions and optimized via backpropagation. The authors also provide theoretical analysis for COIN and prove that it effectively increases the mutual information of node embeddings while being upperbounded by the prior distributions of nodes. The proposed COIN framework is extensively evaluated on various benchmark datasets and tasks to demonstrate its effectiveness. In sensitivity experiments conducted on WebKB, Wisconsin and Wikipedia datasets it was found that COIN performs best when the number of clusters is around the ground truth number of classes. The performance of COIN only has small variances for different coefficients λ for mutual information on Wikipedia datasets. Overall, COIN provides a powerful solution to learning informative node embeddings in bipartite graphs by capturing cluster level information through maximizing mutual information of co-clusters. Its effectiveness has been demonstrated through extensive evaluations on various benchmark datasets and tasks.