# GOOD-D: On Unsupervised Graph Out-Of-Distribution Detection

arXiv: https://arxiv.org/abs/2211.04208 · HTML: https://mlsanity.com/paper/2211.04208/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 65 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 30 of 52)

- [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)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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 Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [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)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [Self-supervised Learning: Generative or Contrastive](https://mlsanity.com/paper/2006.08218/) (2020)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [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)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [FedProto: Federated Prototype Learning across Heterogeneous Clients](https://mlsanity.com/paper/2105.00243/) (2021)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Graph Self-Supervised Learning: A Survey](https://mlsanity.com/paper/2103.00111/) (2021)
- [Deep Anomaly Detection Using Geometric Transformations](https://mlsanity.com/paper/1805.10917/) (2018)
- [SSD: A Unified Framework for Self-Supervised Outlier Detection](https://mlsanity.com/paper/2103.12051/) (2021)
- [Position-aware Graph Neural Networks](https://mlsanity.com/paper/1906.04817/) (2019)

## Built on by (most cited first, 30 of 47)

- [Federated Learning on Non-IID Graphs via Structural Knowledge Sharing](https://mlsanity.com/paper/2211.13009/) (2022)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [A Survey of Graph Neural Networks in Real world: Imbalance, Noise, Privacy and OOD Challenges](https://mlsanity.com/paper/2403.04468/) (2024)
- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Federated Graph Semantic and Structural Learning](https://mlsanity.com/paper/2406.18937/) (2024)
- [Learning Strong Graph Neural Networks with Weak Information](https://mlsanity.com/paper/2305.18457/) (2023)
- [Finding the Missing-half: Graph Complementary Learning for Homophily-prone and Heterophily-prone Graphs](https://mlsanity.com/paper/2306.07608/) (2023)
- [PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection](https://mlsanity.com/paper/2310.11676/) (2023)
- [Optimizing OOD Detection in Molecular Graphs: A Novel Approach with Diffusion Models](https://mlsanity.com/paper/2404.15625/) (2024)
- [Normalizing Flow-based Neural Process for Few-Shot Knowledge Graph Completion](https://mlsanity.com/paper/2304.08183/) (2023)
- [Graph Learning under Distribution Shifts: A Comprehensive Survey on Domain Adaptation, Out-of-distribution, and Continual Learning](https://mlsanity.com/paper/2402.16374/) (2024)
- [Unifying Unsupervised Graph-Level Anomaly Detection and Out-of-Distribution Detection: A Benchmark](https://mlsanity.com/paper/2406.15523/) (2024)
- [GNNEvaluator: Evaluating GNN Performance On Unseen Graphs Without Labels](https://mlsanity.com/paper/2310.14586/) (2023)
- [Subgraph Pooling: Tackling Negative Transfer on Graphs](https://mlsanity.com/paper/2402.08907/) (2024)
- [Graph-level Anomaly Detection via Hierarchical Memory Networks](https://mlsanity.com/paper/2307.00755/) (2023)
- [GOLD: Graph Out-of-Distribution Detection via Implicit Adversarial Latent Generation](https://mlsanity.com/paper/2502.05780/) (2025)
- [CVTGAD: Simplified Transformer with Cross-View Attention for Unsupervised Graph-level Anomaly Detection](https://mlsanity.com/paper/2405.02359/) (2024)
- [LEGO-Learn: Label-Efficient Graph Open-Set Learning](https://mlsanity.com/paper/2410.16386/) (2024)
- [USBD: Universal Structural Basis Distillation for Source-Free Graph Domain Adaptation](https://mlsanity.com/paper/2602.08431/) (2026)
- [SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection](https://mlsanity.com/paper/2310.10237/) (2023)
- [Discriminative Graph-level Anomaly Detection via Dual-students-teacher Model](https://mlsanity.com/paper/2308.01947/) (2023)
- [Few-Shot Causal Representation Learning for Out-of-Distribution Generalization on Heterogeneous Graphs](https://mlsanity.com/paper/2401.03597/) (2024)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [GDDA: Semantic OOD Detection on Graphs under Covariate Shift via Score-Based Diffusion Models](https://mlsanity.com/paper/2410.17526/) (2024)
- [HGOE: Hybrid External and Internal Graph Outlier Exposure for Graph Out-of-Distribution Detection](https://mlsanity.com/paper/2407.21742/) (2024)
- [Multi-representations Space Separation based Graph-level Anomaly-aware Detection](https://mlsanity.com/paper/2307.12994/) (2023)
- [SpectralGap: Graph-Level Out-of-Distribution Detection via Laplacian Eigenvalue Gaps](https://mlsanity.com/paper/2505.15177/) (2025)
- [Learnable Kernel Density Estimation for Graphs and Its Application to Graph-Level Anomaly Detection](https://mlsanity.com/paper/2505.21285/) (2025)
- [Can Molecular Foundation Models Know What They Don't Know? A Simple Remedy with Preference Optimization](https://mlsanity.com/paper/2509.25509/) (2025)

## Abstract (arXiv)

Most existing deep learning models are trained based on the closed-world assumption, where the test data is assumed to be drawn i.i.d. from the same distribution as the training data, known as in-distribution (ID). However, when models are deployed in an open-world scenario, test samples can be out-of-distribution (OOD) and therefore should be handled with caution. To detect such OOD samples drawn from unknown distribution, OOD detection has received increasing attention lately. However, current endeavors mostly focus on grid-structured data and its application for graph-structured data remains under-explored. Considering the fact that data labeling on graphs is commonly time-expensive and labor-intensive, in this work we study the problem of unsupervised graph OOD detection, aiming at detecting OOD graphs solely based on unlabeled ID data. To achieve this goal, we develop a new graph contrastive learning framework GOOD-D for detecting OOD graphs without using any ground-truth labels. By performing hierarchical contrastive learning on the augmented graphs generated by our perturbation-free graph data augmentation method, GOOD-D is able to capture the latent ID patterns and accurately detect OOD graphs based on the semantic inconsistency in different granularities (i.e., node-level, graph-level, and group-level). As a pioneering work in unsupervised graph-level OOD detection, we build a comprehensive benchmark to compare our proposed approach with different state-of-the-art methods. The experiment results demonstrate the superiority of our approach over different methods on various datasets.