# Virtual Node Generation for Node Classification in Sparsely-Labeled Graphs

arXiv: https://arxiv.org/abs/2409.07712 · HTML: https://mlsanity.com/paper/2409.07712/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 44 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 30 of 34)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [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)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [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)
- [GraphMAE: Self-Supervised Masked Graph Autoencoders](https://mlsanity.com/paper/2205.10803/) (2022)
- [Graph Contrastive Learning Automated](https://mlsanity.com/paper/2106.07594/) (2021)
- [Large-Scale Representation Learning on Graphs via Bootstrapping](https://mlsanity.com/paper/2102.06514/) (2021)
- [From Canonical Correlation Analysis to Self-supervised Graph Neural Networks](https://mlsanity.com/paper/2106.12484/) (2021)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [GraphMAE2: A Decoding-Enhanced Masked Self-Supervised Graph Learner](https://mlsanity.com/paper/2304.04779/) (2023)
- [A Unified View on Graph Neural Networks as Graph Signal Denoising](https://mlsanity.com/paper/2010.01777/) (2020)
- [Meta-GNN: On Few-shot Node Classification in Graph Meta-learning](https://mlsanity.com/paper/1905.09718/) (2019)
- [Graph Rationalization with Environment-based Augmentations](https://mlsanity.com/paper/2206.02886/) (2022)
- [Graph Few-shot Learning via Knowledge Transfer](https://mlsanity.com/paper/1910.03053/) (2019)
- [Meta-Learning with Fewer Tasks through Task Interpolation](https://mlsanity.com/paper/2106.02695/) (2021)
- [Task-Adaptive Few-shot Node Classification](https://mlsanity.com/paper/2206.11972/) (2022)
- [Topological Relational Learning on Graphs](https://mlsanity.com/paper/2110.15529/) (2021)
- [Meta Propagation Networks for Graph Few-shot Semi-supervised Learning](https://mlsanity.com/paper/2112.09810/) (2021)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [Transductive Linear Probing: A Novel Framework for Few-Shot Node Classification](https://mlsanity.com/paper/2212.05606/) (2022)
- [Semi-Supervised Graph Imbalanced Regression](https://mlsanity.com/paper/2305.12087/) (2023)
- [Contrastive Meta-Learning for Few-shot Node Classification](https://mlsanity.com/paper/2306.15154/) (2023)

## Abstract (arXiv)

In the broader machine learning literature, data-generation methods demonstrate promising results by generating additional informative training examples via augmenting sparse labels. Such methods are less studied in graphs due to the intricate dependencies among nodes in complex topology structures. This paper presents a novel node generation method that infuses a small set of high-quality synthesized nodes into the graph as additional labeled nodes to optimally expand the propagation of labeled information. By simply infusing additional nodes, the framework is orthogonal to the graph learning and downstream classification techniques, and thus is compatible with most popular graph pre-training (self-supervised learning), semi-supervised learning, and meta-learning methods. The contribution lies in designing the generated node set by solving a novel optimization problem. The optimization places the generated nodes in a manner that: (1) minimizes the classification loss to guarantee training accuracy and (2) maximizes label propagation to low-confidence nodes in the downstream task to ensure high-quality propagation. Theoretically, we show that the above dual optimization maximizes the global confidence of node classification. Our Experiments demonstrate statistically significant performance improvements over 14 baselines on 10 publicly available datasets.