# COIN: Co-Cluster Infomax for Bipartite Graphs

arXiv: https://arxiv.org/abs/2206.00006 · HTML: https://mlsanity.com/paper/2206.00006/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 68 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 30 of 38)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Graph Convolutional Neural Networks for Web-Scale Recommender Systems](https://mlsanity.com/paper/1806.01973/) (2018)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Neural Graph Collaborative Filtering](https://mlsanity.com/paper/1905.08108/) (2019)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Unsupervised Attributed Multiplex Network Embedding](https://mlsanity.com/paper/1911.06750/) (2019)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Adversarially Regularized Graph Autoencoder for Graph Embedding](https://mlsanity.com/paper/1802.04407/) (2018)
- [HDMI: High-order Deep Multiplex Infomax](https://mlsanity.com/paper/2102.07810/) (2021)
- [Graph Learning based Recommender Systems: A Review](https://mlsanity.com/paper/2105.06339/) (2021)
- [Adversarial Graph Contrastive Learning with Information Regularization](https://mlsanity.com/paper/2202.06491/) (2022)
- [Graph Communal Contrastive Learning](https://mlsanity.com/paper/2110.14863/) (2021)

## Built on by (most cited first, 14 of 14)

- [Heterogeneous Contrastive Learning for Foundation Models and Beyond](https://mlsanity.com/paper/2404.00225/) (2024)
- [Hierarchical Multi-Marginal Optimal Transport for Network Alignment](https://mlsanity.com/paper/2310.04470/) (2023)
- [MentorGNN: Deriving Curriculum for Pre-Training GNNs](https://mlsanity.com/paper/2208.09905/) (2022)
- [PyG-SSL: A Graph Self-Supervised Learning Toolkit](https://mlsanity.com/paper/2412.21151/) (2024)
- [Can Graph Neural Networks Learn Language with Extremely Weak Text Supervision?](https://mlsanity.com/paper/2412.08174/) (2024)
- [STERLING: Synergistic Representation Learning on Bipartite Graphs](https://mlsanity.com/paper/2302.05428/) (2023)
- [FairGen: Towards Fair Graph Generation](https://mlsanity.com/paper/2303.17743/) (2023)
- [Causality-Aware Spatiotemporal Graph Neural Networks for Spatiotemporal Time Series Imputation](https://mlsanity.com/paper/2403.11960/) (2024)
- [Joint Optimal Transport and Embedding for Network Alignment](https://mlsanity.com/paper/2502.19334/) (2025)
- [Cluster Aware Graph Anomaly Detection](https://mlsanity.com/paper/2409.09770/) (2024)
- [InterFormer: Effective Heterogeneous Interaction Learning for Click-Through Rate Prediction](https://mlsanity.com/paper/2411.09852/) (2024)
- [ARIEL: Adversarial Graph Contrastive Learning](https://mlsanity.com/paper/2208.06956/) (2022)
- [Automated Contrastive Learning Strategy Search for Time Series](https://mlsanity.com/paper/2403.12641/) (2024)
- [Mixture of Sequence: Theme-Aware Mixture-of-Experts for Long-Sequence Recommendation](https://mlsanity.com/paper/2604.20858/) (2026)

## Abstract (arXiv)

Bipartite graphs are powerful data structures to model interactions between two types of nodes, which have been used in a variety of applications, such as recommender systems, information retrieval, and drug discovery. A fundamental challenge for bipartite graphs is how to learn informative node embeddings. Despite the success of recent self-supervised learning methods on bipartite graphs, their objectives are discriminating instance-wise positive and negative node pairs, which could contain cluster-level errors. In this paper, we introduce a novel co-cluster infomax (COIN) framework, which captures the cluster-level information by maximizing the mutual information of co-clusters. Different from previous infomax methods which estimate mutual information by neural networks, COIN could easily calculate mutual information. Besides, COIN is an end-to-end coclustering method which can be trained jointly with other objective functions and optimized via back-propagation. Furthermore, we also provide theoretical analysis for COIN. We theoretically prove that COIN is able to effectively increase the mutual information of node embeddings and COIN is upper-bounded by the prior distributions of nodes. We extensively evaluate the proposed COIN framework on various benchmark datasets and tasks to demonstrate the effectiveness of COIN.