# Open-Set Graph Anomaly Detection via Normal Structure Regularisation

arXiv: https://arxiv.org/abs/2311.06835 · HTML: https://mlsanity.com/paper/2311.06835/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 62 references that are in the map.
- First posted on arXiv 12 Nov 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Pitfalls of Graph Neural Network Evaluation](https://mlsanity.com/paper/1811.05868/) (2018)
- [Towards Total Recall in Industrial Anomaly Detection](https://mlsanity.com/paper/2106.08265/) (2021)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [Learning Memory-guided Normality for Anomaly Detection](https://mlsanity.com/paper/2003.13228/) (2020)
- [Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters](https://mlsanity.com/paper/2008.08692/) (2020)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Deep Anomaly Detection with Deviation Networks](https://mlsanity.com/paper/1911.08623/) (2019)
- [GraphSMOTE: Imbalanced Node Classification on Graphs with Graph Neural Networks](https://mlsanity.com/paper/2103.08826/) (2021)
- [Learning and Evaluating Representations for Deep One-class Classification](https://mlsanity.com/paper/2011.02578/) (2020)
- [Data Augmentation for Deep Graph Learning: A Survey](https://mlsanity.com/paper/2202.08235/) (2022)
- [Adversarially Learned Anomaly Detection](https://mlsanity.com/paper/1812.02288/) (2018)
- [Few-shot Network Anomaly Detection via Cross-network Meta-learning](https://mlsanity.com/paper/2102.11165/) (2021)
- [Deep Weakly-supervised Anomaly Detection](https://mlsanity.com/paper/1910.13601/) (2019)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [ImGAGN:Imbalanced Network Embedding via Generative Adversarial Graph Networks](https://mlsanity.com/paper/2106.02817/) (2021)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [XGBOD: Improving Supervised Outlier Detection with Unsupervised Representation Learning](https://mlsanity.com/paper/1912.00290/) (2019)
- [Toward Deep Supervised Anomaly Detection: Reinforcement Learning from Partially Labeled Anomaly Data](https://mlsanity.com/paper/2009.06847/) (2020)
- [SpecAE: Spectral AutoEncoder for Anomaly Detection in Attributed Networks](https://mlsanity.com/paper/1908.03849/) (2019)
- [Scalable Anomaly Ranking of Attributed Neighborhoods](https://mlsanity.com/paper/1601.06711/) (2016)

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

- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Zero-shot Generalist Graph Anomaly Detection with Unified Neighborhood Prompts](https://mlsanity.com/paper/2410.14886/) (2024)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [A Survey of Generalization of Graph Anomaly Detection: From Transfer Learning to Foundation Models](https://mlsanity.com/paper/2509.06609/) (2025)
- [Correcting False Alarms from Unseen: Adapting Graph Anomaly Detectors at Test Time](https://mlsanity.com/paper/2511.07023/) (2025)
- [Generalist Graph Anomaly Detection via Prototype-Based Distillation](https://mlsanity.com/paper/2605.26857/) (2026)
- [Towards Anomaly-Aware Pre-Training and Fine-Tuning for Graph Anomaly Detection](https://mlsanity.com/paper/2504.14250/) (2025)
- [Normality Calibration in Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2510.02014/) (2025)
- [CEDL: Centre-Enhanced Discriminative Learning for Anomaly Detection](https://mlsanity.com/paper/2511.12388/) (2025)
- [Open-Set Supervised 3D Anomaly Detection: An Industrial Dataset and a Generalisable Framework for Unknown Defects](https://mlsanity.com/paper/2604.01171/) (2026)
- [The Selection Rule Decides the Winner: A Pre-Registered Audit of Open-Set Graph Anomaly Detection](https://mlsanity.com/paper/2609.33370/) (2026)

## Abstract (arXiv)

This paper considers an important Graph Anomaly Detection (GAD) task, namely open-set GAD, which aims to train a detection model using a small number of normal and anomaly nodes (referred to as seen anomalies) to detect both seen anomalies and unseen anomalies (i.e., anomalies that cannot be illustrated the training anomalies). Those labelled training data provide crucial prior knowledge about abnormalities for GAD models, enabling substantially reduced detection errors. However, current supervised GAD methods tend to over-emphasise fitting the seen anomalies, leading to many errors of detecting the unseen anomalies as normal nodes. Further, existing open-set AD models were introduced to handle Euclidean data, failing to effectively capture discriminative features from graph structure and node attributes for GAD. In this work, we propose a novel open-set GAD approach, namely normal structure regularisation (NSReg), to achieve generalised detection ability to unseen anomalies, while maintaining its effectiveness on detecting seen anomalies. The key idea in NSReg is to introduce a regularisation term that enforces the learning of compact, semantically-rich representations of normal nodes based on their structural relations to other nodes. When being optimised with supervised anomaly detection losses, the regularisation term helps incorporate strong normality into the modelling, and thus, it effectively avoids over-fitting the seen anomalies and learns a better normality decision boundary, largely reducing the false negatives of detecting unseen anomalies as normal. Extensive empirical results on seven real-world datasets show that NSReg significantly outperforms state-of-the-art competing methods by at least 14% AUC-ROC on the unseen anomaly classes and by 10% AUC-ROC on all anomaly classes.