# Alleviating Structural Distribution Shift in Graph Anomaly Detection

arXiv: https://arxiv.org/abs/2401.14155 · HTML: https://mlsanity.com/paper/2401.14155/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 53 references that are in the map.
- First posted on arXiv 25 Jan 2024.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [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)
- [GraphLIME: Local Interpretable Model Explanations for Graph Neural Networks](https://mlsanity.com/paper/2001.06216/) (2020)
- [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)
- [Counterfactual Samples Synthesizing for Robust Visual Question Answering](https://mlsanity.com/paper/2003.06576/) (2020)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Unifying Graph Convolutional Neural Networks and Label Propagation](https://mlsanity.com/paper/2002.06755/) (2020)
- [Shift-Robust GNNs: Overcoming the Limitations of Localized Graph Training Data](https://mlsanity.com/paper/2108.01099/) (2021)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [Subgroup Generalization and Fairness of Graph Neural Networks](https://mlsanity.com/paper/2106.15535/) (2021)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [GCN-Based User Representation Learning for Unifying Robust Recommendation and Fraudster Detection](https://mlsanity.com/paper/2005.10150/) (2020)
- [Causal Understanding of Fake News Dissemination on Social Media](https://mlsanity.com/paper/2010.10580/) (2020)
- [F-FADE: Frequency Factorization for Anomaly Detection in Edge Streams](https://mlsanity.com/paper/2011.04723/) (2020)
- [Debiased Graph Neural Networks with Agnostic Label Selection Bias](https://mlsanity.com/paper/2201.07708/) (2022)
- [Instance-Dependent PU Learning by Bayesian Optimal Relabeling](https://mlsanity.com/paper/1808.02180/) (2018)
- [Rumor Detection with Self-supervised Learning on Texts and Social Graph](https://mlsanity.com/paper/2204.08838/) (2022)
- [Semi-supervised Embedding in Attributed Networks with Outliers](https://mlsanity.com/paper/1703.08100/) (2017)
- [When Does A Spectral Graph Neural Network Fail in Node Classification?](https://mlsanity.com/paper/2202.07902/) (2022)

## Built on by (most cited first, 30 of 32)

- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [Partitioning Message Passing for Graph Fraud Detection](https://mlsanity.com/paper/2412.00020/) (2024)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [EXGC: Bridging Efficiency and Explainability in Graph Condensation](https://mlsanity.com/paper/2402.05962/) (2024)
- [Anomaly Detection in Dynamic Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2406.00134/) (2024)
- [A Survey of Generalization of Graph Anomaly Detection: From Transfer Learning to Foundation Models](https://mlsanity.com/paper/2509.06609/) (2025)
- [Can LLMs Find Fraudsters? Multi-level LLM Enhanced Graph Fraud Detection](https://mlsanity.com/paper/2507.11997/) (2025)
- [Lower-Left Partial AUC: An Effective and Efficient Optimization Metric for Recommendation](https://mlsanity.com/paper/2403.00844/) (2024)
- [DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector](https://mlsanity.com/paper/2410.06549/) (2024)
- [Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shifts](https://mlsanity.com/paper/2408.09490/) (2024)
- [Improving Expressive Power of Spectral Graph Neural Networks with Eigenvalue Correction](https://mlsanity.com/paper/2401.15603/) (2024)
- [Generation is better than Modification: Combating High Class Homophily Variance in Graph Anomaly Detection](https://mlsanity.com/paper/2403.10339/) (2024)
- [Causal invariant geographic network representations with feature and structural distribution shifts](https://mlsanity.com/paper/2503.19382/) (2025)
- [Global Confidence Degree Based Graph Neural Network for Financial Fraud Detection](https://mlsanity.com/paper/2407.17333/) (2024)
- [Partition-wise Graph Filtering: A Unified Perspective Through the Lens of Graph Coarsening](https://mlsanity.com/paper/2505.14033/) (2025)
- [Polynomial Selection in Spectral Graph Neural Networks: An Error-Sum of Function Slices Approach](https://mlsanity.com/paper/2404.15354/) (2024)
- [NeiGAD: Augmenting Graph Anomaly Detection via Spectral Neighbor Information](https://mlsanity.com/paper/2603.28300/) (2026)
- [Detect by Yourself: Self-Designing Agentic Workflows for Few-Shot Graph Anomaly Detection](https://mlsanity.com/paper/2605.27470/) (2026)
- [Towards Understanding Link Predictor Generalizability Under Distribution Shifts](https://mlsanity.com/paper/2406.08788/) (2024)
- [Balanced Edge Pruning for Graph Anomaly Detection with Noisy Labels](https://mlsanity.com/paper/2407.05934/) (2024)
- [High-Pass Graph Convolutional Network for Enhanced Anomaly Detection: A Novel Approach](https://mlsanity.com/paper/2411.01817/) (2024)
- [Reconciling Attribute and Structural Anomalies for Improved Graph Anomaly Detection](https://mlsanity.com/paper/2506.23469/) (2025)
- [Subgraph Generation for Generalizing on Out-of-Distribution Links](https://mlsanity.com/paper/2507.11710/) (2025)
- [CRoC: Context Refactoring Contrast for Graph Anomaly Detection with Limited Supervision](https://mlsanity.com/paper/2508.12278/) (2025)
- [Addressing Graph Anomaly Detection via Causal Edge Separation and Spectrum](https://mlsanity.com/paper/2508.14684/) (2025)
- [Normality Calibration in Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2510.02014/) (2025)
- [Federated Graph AGI for Cross-Border Insider Threat Intelligence in Government Financial Schemes](https://mlsanity.com/paper/2602.16109/) (2026)
- [Neuromorphic Graph Anomaly Detection via Adaptive STDP and Spiking Graph Neural Networks](https://mlsanity.com/paper/2605.13863/) (2026)

## Abstract (arXiv)

Graph anomaly detection (GAD) is a challenging binary classification problem due to its different structural distribution between anomalies and normal nodes -- abnormal nodes are a minority, therefore holding high heterophily and low homophily compared to normal nodes. Furthermore, due to various time factors and the annotation preferences of human experts, the heterophily and homophily can change across training and testing data, which is called structural distribution shift (SDS) in this paper. The mainstream methods are built on graph neural networks (GNNs), benefiting the classification of normals from aggregating homophilous neighbors, yet ignoring the SDS issue for anomalies and suffering from poor generalization. This work solves the problem from a feature view. We observe that the degree of SDS varies between anomalies and normal nodes. Hence to address the issue, the key lies in resisting high heterophily for anomalies meanwhile benefiting the learning of normals from homophily. We tease out the anomaly features on which we constrain to mitigate the effect of heterophilous neighbors and make them invariant. We term our proposed framework as Graph Decomposition Network (GDN). Extensive experiments are conducted on two benchmark datasets, and the proposed framework achieves a remarkable performance boost in GAD, especially in an SDS environment where anomalies have largely different structural distribution across training and testing environments. Codes are open-sourced in https://github.com/blacksingular/wsdm_GDN.