# Learning Graph Neural Networks with Positive and Unlabeled Nodes

arXiv: https://arxiv.org/abs/2103.04683 · HTML: https://mlsanity.com/paper/2103.04683/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 8 Mar 2021.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Graph Transformer Networks](https://mlsanity.com/paper/1911.06455/) (2019)
- [Empirical Evaluation of Rectified Activations in Convolutional Network](https://mlsanity.com/paper/1505.00853/) (2015)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Graph Convolutional Policy Network for Goal-Directed Molecular Graph Generation](https://mlsanity.com/paper/1806.02473/) (2018)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings](https://mlsanity.com/paper/2006.13009/) (2020)
- [Design Space for Graph Neural Networks](https://mlsanity.com/paper/2011.08843/) (2020)
- [GaAN: Gated Attention Networks for Learning on Large and Spatiotemporal Graphs](https://mlsanity.com/paper/1803.07294/) (2018)
- [Adaptive Graph Convolutional Neural Networks](https://mlsanity.com/paper/1801.03226/) (2018)
- [Attributed Graph Clustering: A Deep Attentional Embedding Approach](https://mlsanity.com/paper/1906.06532/) (2019)
- [Adversarially Regularized Graph Autoencoder for Graph Embedding](https://mlsanity.com/paper/1802.04407/) (2018)
- [Learning Graph Embedding with Adversarial Training Methods](https://mlsanity.com/paper/1901.01250/) (2019)
- [Semi-supervised User Geolocation via Graph Convolutional Networks](https://mlsanity.com/paper/1804.08049/) (2018)
- [Estimating the class prior and posterior from noisy positives and unlabeled data](https://mlsanity.com/paper/1606.08561/) (2016)
- [Graph Convolutional Networks for Classification with a Structured Label Space](https://mlsanity.com/paper/1710.04908/) (2017)

## Built on by (most cited first, 11 of 11)

- [Generative and Contrastive Self-Supervised Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2108.09896/) (2021)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Towards Graph Self-Supervised Learning with Contrastive Adjusted Zooming](https://mlsanity.com/paper/2111.10698/) (2021)
- [A Comprehensive Survey on Distributed Training of Graph Neural Networks](https://mlsanity.com/paper/2211.05368/) (2022)
- [SecGNN: Privacy-Preserving Graph Neural Network Training and Inference as a Cloud Service](https://mlsanity.com/paper/2202.07835/) (2022)
- [Positive-Unlabeled Node Classification with Structure-aware Graph Learning](https://mlsanity.com/paper/2310.13538/) (2023)
- [Novel Representation Learning Technique using Graphs for Performance Analytics](https://mlsanity.com/paper/2401.10799/) (2024)
- [Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learning](https://mlsanity.com/paper/2405.19919/) (2024)
- [PU GNN: Chargeback Fraud Detection in P2E MMORPGs via Graph Attention Networks with Imbalanced PU Labels](https://mlsanity.com/paper/2211.08604/) (2022)
- [Rethinking the Graph Polynomial Filter via Positive and Negative Coupling Analysis](https://mlsanity.com/paper/2404.10353/) (2024)
- [Quantum Topological Graph Neural Networks for Detecting Complex Fraud Patterns](https://mlsanity.com/paper/2512.03696/) (2025)

## Abstract (arXiv)

Graph neural networks (GNNs) are important tools for transductive learning tasks, such as node classification in graphs, due to their expressive power in capturing complex interdependency between nodes. To enable graph neural network learning, existing works typically assume that labeled nodes, from two or multiple classes, are provided, so that a discriminative classifier can be learned from the labeled data. In reality, this assumption might be too restrictive for applications, as users may only provide labels of interest in a single class for a small number of nodes. In addition, most GNN models only aggregate information from short distances (e.g., 1-hop neighbors) in each round, and fail to capture long distance relationship in graphs. In this paper, we propose a novel graph neural network framework, long-short distance aggregation networks (LSDAN), to overcome these limitations. By generating multiple graphs at different distance levels, based on the adjacency matrix, we develop a long-short distance attention model to model these graphs. The direct neighbors are captured via a short-distance attention mechanism, and neighbors with long distance are captured by a long distance attention mechanism. Two novel risk estimators are further employed to aggregate long-short-distance networks, for PU learning and the loss is back-propagated for model learning. Experimental results on real-world datasets demonstrate the effectiveness of our algorithm.