# Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection

arXiv: https://arxiv.org/abs/2306.00006 · HTML: https://mlsanity.com/paper/2306.00006/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 70 references that are in the map.
- First posted on arXiv 29 May 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [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)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [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)
- [Graph Representation Learning via Graphical Mutual Information Maximization](https://mlsanity.com/paper/2002.01169/) (2020)
- [Graph Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (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)
- [Is Homophily a Necessity for Graph Neural Networks?](https://mlsanity.com/paper/2106.06134/) (2021)
- [Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2103.00113/) (2021)
- [Graph Neural Networks for Graphs with Heterophily: A Survey](https://mlsanity.com/paper/2202.07082/) (2022)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [AnomalyDAE: Dual autoencoder for anomaly detection on attributed networks](https://mlsanity.com/paper/2002.03665/) (2020)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [Generative and Contrastive Self-Supervised Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2108.09896/) (2021)
- [Fast Gradient Attack on Network Embedding](https://mlsanity.com/paper/1809.02797/) (2018)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [GCN-Based User Representation Learning for Unifying Robust Recommendation and Fraudster Detection](https://mlsanity.com/paper/2005.10150/) (2020)
- [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)
- [Hop-Count Based Self-Supervised Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/2104.07917/) (2021)
- [Cross-Domain Graph Anomaly Detection via Anomaly-aware Contrastive Alignment](https://mlsanity.com/paper/2212.01096/) (2022)
- [Reconstruction Enhanced Multi-View Contrastive Learning for Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/2205.04816/) (2022)

## Built on by (most cited first, 30 of 43)

- [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)
- [BlindGuard: Safeguarding LLM-based Multi-Agent Systems under Unknown Attacks](https://mlsanity.com/paper/2508.08127/) (2025)
- [Zero-shot Generalist Graph Anomaly Detection with Unified Neighborhood Prompts](https://mlsanity.com/paper/2410.14886/) (2024)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [Graph-level Anomaly Detection via Hierarchical Memory Networks](https://mlsanity.com/paper/2307.00755/) (2023)
- [Open-Set Graph Anomaly Detection via Normal Structure Regularisation](https://mlsanity.com/paper/2311.06835/) (2023)
- [SmoothGNN: Smoothing-aware GNN for Unsupervised Node Anomaly Detection](https://mlsanity.com/paper/2405.17525/) (2024)
- [FreeGAD: A Training-Free yet Effective Approach for Graph Anomaly Detection](https://mlsanity.com/paper/2508.10594/) (2025)
- [Cluster Aware Graph Anomaly Detection](https://mlsanity.com/paper/2409.09770/) (2024)
- [From Few-Shot to Zero-Shot: Towards Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2602.18793/) (2026)
- [Towards Anomaly Detection on Relational Data](https://mlsanity.com/paper/2606.18621/) (2026)
- [Semi-supervised Graph Anomaly Detection via Robust Homophily Learning](https://mlsanity.com/paper/2506.15448/) (2025)
- [Grad: Guided Relation Diffusion Generation for Graph Augmentation in Graph Fraud Detection](https://mlsanity.com/paper/2512.18133/) (2025)
- [GCTAM: Global and Contextual Truncated Affinity Combined Maximization Model For Unsupervised Graph Anomaly Detection](https://mlsanity.com/paper/2603.01806/) (2026)
- [CAMERA: Adapting to Semantic Camouflage in Unsupervised Text-Attributed Graph Fraud Detection](https://mlsanity.com/paper/2605.20032/) (2026)
- [Coupled-Space Attacks against Random-Walk-based Anomaly Detection](https://mlsanity.com/paper/2307.14387/) (2023)
- [HRGCN: Heterogeneous Graph-level Anomaly Detection with Hierarchical Relation-augmented Graph Neural Networks](https://mlsanity.com/paper/2308.14340/) (2023)
- [UMGAD: Unsupervised Multiplex Graph Anomaly Detection](https://mlsanity.com/paper/2411.12556/) (2024)
- [Cross-Domain Graph Anomaly Detection via Test-Time Training with Homophily-Guided Self-Supervision](https://mlsanity.com/paper/2502.14293/) (2025)
- [OWLEYE: Zero-Shot Learner for Cross-Domain Graph Data Anomaly Detection](https://mlsanity.com/paper/2601.19102/) (2026)
- [PieClam: A Universal Graph Autoencoder Based on Overlapping Inclusive and Exclusive Communities](https://mlsanity.com/paper/2409.11618/) (2024)
- [GrokFormer: Graph Fourier Kolmogorov-Arnold Transformers](https://mlsanity.com/paper/2411.17296/) (2024)
- [AC2L-GAD: Active Counterfactual Contrastive Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2601.21171/) (2026)
- [Generalist Graph Anomaly Detection via Prototype-Based Distillation](https://mlsanity.com/paper/2605.26857/) (2026)
- [When Agents Go Rogue: Activation-Based Detection of Malicious Behaviors in Multi-Agent Systems](https://mlsanity.com/paper/2607.06807/) (2026)
- [Balanced Edge Pruning for Graph Anomaly Detection with Noisy Labels](https://mlsanity.com/paper/2407.05934/) (2024)
- [Towards Anomaly-Aware Pre-Training and Fine-Tuning for Graph Anomaly Detection](https://mlsanity.com/paper/2504.14250/) (2025)
- [CRoC: Context Refactoring Contrast for Graph Anomaly Detection with Limited Supervision](https://mlsanity.com/paper/2508.12278/) (2025)

## Abstract (arXiv)

We reveal a one-class homophily phenomenon, which is one prevalent property we find empirically in real-world graph anomaly detection (GAD) datasets, i.e., normal nodes tend to have strong connection/affinity with each other, while the homophily in abnormal nodes is significantly weaker than normal nodes. However, this anomaly-discriminative property is ignored by existing GAD methods that are typically built using a conventional anomaly detection objective, such as data reconstruction. In this work, we explore this property to introduce a novel unsupervised anomaly scoring measure for GAD, local node affinity, that assigns a larger anomaly score to nodes that are less affiliated with their neighbors, with the affinity defined as similarity on node attributes/representations. We further propose Truncated Affinity Maximization (TAM) that learns tailored node representations for our anomaly measure by maximizing the local affinity of nodes to their neighbors. Optimizing on the original graph structure can be biased by nonhomophily edges (i.e., edges connecting normal and abnormal nodes). Thus, TAM is instead optimized on truncated graphs where non-homophily edges are removed iteratively to mitigate this bias. The learned representations result in significantly stronger local affinity for normal nodes than abnormal nodes. Extensive empirical results on 10 real-world GAD datasets show that TAM substantially outperforms seven competing models, achieving over 10% increase in AUROC/AUPRC compared to the best contenders on challenging datasets. Our code is available at https://github.com/mala-lab/TAM-master/.