# Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification

arXiv: https://arxiv.org/abs/2402.09600 · HTML: https://mlsanity.com/paper/2402.09600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 64 of its 85 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 30 of 64)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (2019)
- [Wiki-CS: A Wikipedia-Based Benchmark for Graph Neural Networks](https://mlsanity.com/paper/2007.02901/) (2020)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Adversarial Graph Augmentation to Improve Graph Contrastive Learning](https://mlsanity.com/paper/2106.05819/) (2021)

## Built on by (most cited first, 1 of 1)

- [Multistage non-deterministic classification using secondary concept graphs and graph convolutional networks for high-level feature extraction](https://mlsanity.com/paper/2411.06212/) (2024)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved remarkable success in learning node representations and have shown strong performance in tasks such as node classification. However, recent findings indicate that the presence of noise in real-world graph data can substantially impair the effectiveness of GNNs. To address this challenge, we introduce a robust and innovative node representation learning method named Graph Contrastive Learning with Low-Rank Regularization, or GCL-LRR, which follows a two-stage transductive learning framework for node classification. In the first stage, the GCL-LRR encoder is optimized through prototypical contrastive learning while incorporating a low-rank regularization objective. In the second stage, the representations generated by GCL-LRR are employed by a linear transductive classifier to predict the labels of unlabeled nodes within the graph. Our GCL-LRR is inspired by the Low Frequency Property (LFP) of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. To the best of our knowledge, our theoretical result is among the first to theoretically demonstrate the advantage of low-rank regularization in transductive learning, which is also supported by strong empirical results. To further enhance the performance of GCL-LRR, we present an improved model named GCL-LR-Attention, which incorporates a novel LR-Attention layer into GCL-LRR. GCL-LR-Attention reduces the kernel complexity of GCL-LRR and contributes to a tighter generalization bound, leading to improved performance. Extensive evaluations on standard benchmark datasets evidence the effectiveness and robustness of both GCL-LRR and GCL-LR-Attention in learning meaningful node representations. The code is available at https://github.com/Statistical-Deep-Learning/GCL-LR-Attention.