# From Canonical Correlation Analysis to Self-supervised Graph Neural Networks

arXiv: https://arxiv.org/abs/2106.12484 · HTML: https://mlsanity.com/paper/2106.12484/

## Key facts

- Cited by 141 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 67 references that are in the map.
- First posted on arXiv 23 Jun 2021.

## Builds on (most cited first, 30 of 41)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Learning deep representations by mutual information estimation and maximization](https://mlsanity.com/paper/1808.06670/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Approximate Nearest Neighbor Negative Contrastive Learning for Dense Text Retrieval](https://mlsanity.com/paper/2007.00808/) (2020)
- [Deep Learning and the Information Bottleneck Principle](https://mlsanity.com/paper/1503.02406/) (2015)
- [Image-based Recommendations on Styles and Substitutes](https://mlsanity.com/paper/1506.04757/) (2015)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Contrastive Multi-View Representation Learning on Graphs](https://mlsanity.com/paper/2006.05582/) (2020)
- [Deep Graph Contrastive Representation Learning](https://mlsanity.com/paper/2006.04131/) (2020)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Diffusion Improves Graph Learning](https://mlsanity.com/paper/1911.05485/) (2019)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)

## Built on by (most cited first, 30 of 141)

- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [LLaGA: Large Language and Graph Assistant](https://mlsanity.com/paper/2402.08170/) (2024)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [What's Behind the Mask: Understanding Masked Graph Modeling for Graph Autoencoders](https://mlsanity.com/paper/2205.10053/) (2022)
- [ProGCL: Rethinking Hard Negative Mining in Graph Contrastive Learning](https://mlsanity.com/paper/2110.02027/) (2021)
- [Graph Mixture of Experts: Learning on Large-Scale Graphs with Explicit Diversity Modeling](https://mlsanity.com/paper/2304.02806/) (2023)
- [Graph Data Augmentation for Graph Machine Learning: A Survey](https://mlsanity.com/paper/2202.08871/) (2022)
- [Heterogeneous Graph Masked Autoencoders](https://mlsanity.com/paper/2208.09957/) (2022)
- [Revisiting Graph Contrastive Learning from the Perspective of Graph Spectrum](https://mlsanity.com/paper/2210.02330/) (2022)
- [Generalized Graph Prompt: Toward a Unification of Pre-Training and Downstream Tasks on Graphs](https://mlsanity.com/paper/2311.15317/) (2023)
- [Simple and Asymmetric Graph Contrastive Learning without Augmentations](https://mlsanity.com/paper/2310.18884/) (2023)
- [Multi-task Self-supervised Graph Neural Networks Enable Stronger Task Generalization](https://mlsanity.com/paper/2210.02016/) (2022)
- [Uncovering the Structural Fairness in Graph Contrastive Learning](https://mlsanity.com/paper/2210.03011/) (2022)
- [A Survey of Pretraining on Graphs: Taxonomy, Methods, and Applications](https://mlsanity.com/paper/2202.07893/) (2022)
- [SeeGera: Self-supervised Semi-implicit Graph Variational Auto-encoders with Masking](https://mlsanity.com/paper/2301.12458/) (2023)
- [Counterfactual Learning on Graphs: A Survey](https://mlsanity.com/paper/2304.01391/) (2023)
- [Graph-level Representation Learning with Joint-Embedding Predictive Architectures](https://mlsanity.com/paper/2309.16014/) (2023)
- [Rethinking Graph Masked Autoencoders through Alignment and Uniformity](https://mlsanity.com/paper/2402.07225/) (2024)
- [ImGCL: Revisiting Graph Contrastive Learning on Imbalanced Node Classification](https://mlsanity.com/paper/2205.11332/) (2022)
- [An Investigation into Whitening Loss for Self-supervised Learning](https://mlsanity.com/paper/2210.03586/) (2022)
- [Augmentation-Free Graph Contrastive Learning of Invariant-Discriminative Representations](https://mlsanity.com/paper/2210.08345/) (2022)
- [GraphLoRA: Structure-Aware Contrastive Low-Rank Adaptation for Cross-Graph Transfer Learning](https://mlsanity.com/paper/2409.16670/) (2024)
- [SpeGCL: Self-supervised Graph Spectrum Contrastive Learning without Positive Samples](https://mlsanity.com/paper/2410.10365/) (2024)
- [GATE: Graph CCA for Temporal SElf-supervised Learning for Label-efficient fMRI Analysis](https://mlsanity.com/paper/2203.09034/) (2022)
- [HomoGCL: Rethinking Homophily in Graph Contrastive Learning](https://mlsanity.com/paper/2306.09614/) (2023)
- [GAugLLM: Improving Graph Contrastive Learning for Text-Attributed Graphs with Large Language Models](https://mlsanity.com/paper/2406.11945/) (2024)
- [Graph Soft-Contrastive Learning via Neighborhood Ranking](https://mlsanity.com/paper/2209.13964/) (2022)
- [GraphAlign: Pretraining One Graph Neural Network on Multiple Graphs via Feature Alignment](https://mlsanity.com/paper/2406.02953/) (2024)
- [Wiener Graph Deconvolutional Network Improves Graph Self-Supervised Learning](https://mlsanity.com/paper/2206.12933/) (2022)
- [Directional diffusion models for graph representation learning](https://mlsanity.com/paper/2306.13210/) (2023)

## Abstract (arXiv)

We introduce a conceptually simple yet effective model for self-supervised representation learning with graph data. It follows the previous methods that generate two views of an input graph through data augmentation. However, unlike contrastive methods that focus on instance-level discrimination, we optimize an innovative feature-level objective inspired by classical Canonical Correlation Analysis. Compared with other works, our approach requires none of the parameterized mutual information estimator, additional projector, asymmetric structures, and most importantly, negative samples which can be costly. We show that the new objective essentially 1) aims at discarding augmentation-variant information by learning invariant representations, and 2) can prevent degenerated solutions by decorrelating features in different dimensions. Our theoretical analysis further provides an understanding for the new objective which can be equivalently seen as an instantiation of the Information Bottleneck Principle under the self-supervised setting. Despite its simplicity, our method performs competitively on seven public graph datasets. The code is available at: https://github.com/hengruizhang98/CCA-SSG.