# Graph Representation Learning via Graphical Mutual Information Maximization

arXiv: https://arxiv.org/abs/2002.01169 · HTML: https://mlsanity.com/paper/2002.01169/

## Key facts

- Cited by 217 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2020.

## Built on by (most cited first, 30 of 217)

- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [Self-Supervised Learning of Graph Neural Networks: A Unified Review](https://mlsanity.com/paper/2102.10757/) (2021)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [GraphPrompt: Unifying Pre-Training and Downstream Tasks for Graph Neural Networks](https://mlsanity.com/paper/2302.08043/) (2023)
- [Motif-based Graph Self-Supervised Learning for Molecular Property Prediction](https://mlsanity.com/paper/2110.00987/) (2021)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Self-supervised Learning on Graphs: Contrastive, Generative,or Predictive](https://mlsanity.com/paper/2105.07342/) (2021)
- [Self-supervised Heterogeneous Graph Neural Network with Co-contrastive Learning](https://mlsanity.com/paper/2105.09111/) (2021)
- [Towards Unsupervised Deep Graph Structure Learning](https://mlsanity.com/paper/2201.06367/) (2022)
- [An Empirical Study of Graph Contrastive Learning](https://mlsanity.com/paper/2109.01116/) (2021)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Improving Graph Collaborative Filtering with Neighborhood-enriched Contrastive Learning](https://mlsanity.com/paper/2202.06200/) (2022)
- [HDMI: High-order Deep Multiplex Infomax](https://mlsanity.com/paper/2102.07810/) (2021)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [ProGCL: Rethinking Hard Negative Mining in Graph Contrastive Learning](https://mlsanity.com/paper/2110.02027/) (2021)
- [LightGCL: Simple Yet Effective Graph Contrastive Learning for Recommendation](https://mlsanity.com/paper/2302.08191/) (2023)
- [Multi-Scale Contrastive Siamese Networks for Self-Supervised Graph Representation Learning](https://mlsanity.com/paper/2105.05682/) (2021)
- [Rethinking and Scaling Up Graph Contrastive Learning: An Extremely Efficient Approach with Group Discrimination](https://mlsanity.com/paper/2206.01535/) (2022)
- [A Survey on Graph Representation Learning Methods](https://mlsanity.com/paper/2204.01855/) (2022)
- [Graph Prompt Learning: A Comprehensive Survey and Beyond](https://mlsanity.com/paper/2311.16534/) (2023)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Spectral Feature Augmentation for Graph Contrastive Learning and Beyond](https://mlsanity.com/paper/2212.01026/) (2022)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Unsupervised Path Representation Learning with Curriculum Negative Sampling](https://mlsanity.com/paper/2106.09373/) (2021)
- [COSTA: Covariance-Preserving Feature Augmentation for Graph Contrastive Learning](https://mlsanity.com/paper/2206.04726/) (2022)
- [Spectral Augmentation for Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2210.00643/) (2022)

## Abstract (arXiv)

The richness in the content of various information networks such as social networks and communication networks provides the unprecedented potential for learning high-quality expressive representations without external supervision. This paper investigates how to preserve and extract the abundant information from graph-structured data into embedding space in an unsupervised manner. To this end, we propose a novel concept, Graphical Mutual Information (GMI), to measure the correlation between input graphs and high-level hidden representations. GMI generalizes the idea of conventional mutual information computations from vector space to the graph domain where measuring mutual information from two aspects of node features and topological structure is indispensable. GMI exhibits several benefits: First, it is invariant to the isomorphic transformation of input graphs---an inevitable constraint in many existing graph representation learning algorithms; Besides, it can be efficiently estimated and maximized by current mutual information estimation methods such as MINE; Finally, our theoretical analysis confirms its correctness and rationality. With the aid of GMI, we develop an unsupervised learning model trained by maximizing GMI between the input and output of a graph neural encoder. Considerable experiments on transductive as well as inductive node classification and link prediction demonstrate that our method outperforms state-of-the-art unsupervised counterparts, and even sometimes exceeds the performance of supervised ones.