# Self-supervised Learning and Graph Classification under Heterophily

arXiv: https://arxiv.org/abs/2306.08469 · HTML: https://mlsanity.com/paper/2306.08469/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [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)
- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [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)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [GPT-GNN: Generative Pre-Training of Graph Neural Networks](https://mlsanity.com/paper/2006.15437/) (2020)
- [DeeperGCN: All You Need to Train Deeper GCNs](https://mlsanity.com/paper/2006.07739/) (2020)
- [struc2vec: Learning Node Representations from Structural Identity](https://mlsanity.com/paper/1704.03165/) (2017)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2102.06462/) (2021)
- [Self-supervised Graph-level Representation Learning with Local and Global Structure](https://mlsanity.com/paper/2106.04113/) (2021)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Label Efficient Semi-Supervised Learning via Graph Filtering](https://mlsanity.com/paper/1901.09993/) (2019)
- [Pairwise Half-graph Discrimination: A Simple Graph-level Self-supervised Strategy for Pre-training Graph Neural Networks](https://mlsanity.com/paper/2110.13567/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Survey on Learning from Graphs with Heterophily: Recent Advances and Future Directions](https://mlsanity.com/paper/2401.09769/) (2024)
- [Learn from Heterophily: Heterophilous Information-enhanced Graph Neural Network](https://mlsanity.com/paper/2403.17351/) (2024)

## Abstract (arXiv)

Self-supervised learning has shown its promising capability in graph representation learning in recent work. Most existing pre-training strategies usually choose the popular Graph neural networks (GNNs), which can be seen as a special form of low-pass filter, fail to effectively capture heterophily. In this paper, we first present an experimental investigation exploring the performance of low-pass and high-pass filters in heterophily graph classification, where the results clearly show that high-frequency signal is important for learning heterophily graph representation. On the other hand, it is still unclear how to effectively capture the structural pattern of graphs and how to measure the capability of the self-supervised pre-training strategy in capturing graph structure. To address the problem, we first design a quantitative metric to Measure Graph Structure (MGS), which analyzes correlation between structural similarity and embedding similarity of graph pairs. Then, to enhance the graph structural information captured by self-supervised learning, we propose a novel self-supervised strategy for Pre-training GNNs based on the Metric (PGM). Extensive experiments validate our pre-training strategy achieves state-of-the-art performance for molecular property prediction and protein function prediction. In addition, we find choosing the suitable filter sometimes may be better than designing good pre-training strategies for heterophily graph classification.