# Unsupervised Graph Anomaly Detection via Multi-Hypersphere Heterophilic Graph Learning

arXiv: https://arxiv.org/abs/2503.12037 · HTML: https://mlsanity.com/paper/2503.12037/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 15 Mar 2025.

## Builds on (most cited first, 30 of 32)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [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 Neural Networks with Heterophily](https://mlsanity.com/paper/2009.13566/) (2020)
- [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)
- [Structural Deep Clustering Network](https://mlsanity.com/paper/2002.01633/) (2020)
- [Augmentation-Free Self-Supervised Learning on Graphs](https://mlsanity.com/paper/2112.02472/) (2021)
- [Mean-Shifted Contrastive Loss for Anomaly Detection](https://mlsanity.com/paper/2106.03844/) (2021)
- [AnomalyDAE: Dual autoencoder for anomaly detection on attributed networks](https://mlsanity.com/paper/2002.03665/) (2020)
- [BOND: Benchmarking Unsupervised Outlier Node Detection on Static Attributed Graphs](https://mlsanity.com/paper/2206.10071/) (2022)
- [Beyond Smoothing: Unsupervised Graph Representation Learning with Edge Heterophily Discriminating](https://mlsanity.com/paper/2211.14065/) (2022)
- [Graph Anomaly Detection via Multi-Scale Contrastive Learning Networks with Augmented View](https://mlsanity.com/paper/2212.00535/) (2022)
- [Raising the Bar in Graph-level Anomaly Detection](https://mlsanity.com/paper/2205.13845/) (2022)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Deep Robust Clustering by Contrastive Learning](https://mlsanity.com/paper/2008.03030/) (2020)
- [Curvature Graph Neural Network](https://mlsanity.com/paper/2106.15762/) (2021)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [Graph Anomaly Detection with Graph Neural Networks: Current Status and Challenges](https://mlsanity.com/paper/2209.14930/) (2022)
- [ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection](https://mlsanity.com/paper/2312.14535/) (2023)
- [Semi-supervised Anomaly Detection on Attributed Graphs](https://mlsanity.com/paper/2002.12011/) (2020)
- [AntiBenford Subgraphs: Unsupervised Anomaly Detection in Financial Networks](https://mlsanity.com/paper/2205.13426/) (2022)
- [Unsupervised Graph Outlier Detection: Problem Revisit, New Insight, and Superior Method](https://mlsanity.com/paper/2210.12941/) (2022)
- [From Unsupervised to Few-shot Graph Anomaly Detection: A Multi-scale Contrastive Learning Approach](https://mlsanity.com/paper/2202.05525/) (2022)
- [Higher-order Structure Based Anomaly Detection on Attributed Networks](https://mlsanity.com/paper/2406.04690/) (2024)

## Abstract (arXiv)

Graph Anomaly Detection (GAD) plays a vital role in various data mining applications such as e-commerce fraud prevention and malicious user detection. Recently, Graph Neural Network (GNN) based approach has demonstrated great effectiveness in GAD by first encoding graph data into low-dimensional representations and then identifying anomalies under the guidance of supervised or unsupervised signals. However, existing GNN-based approaches implicitly follow the homophily principle (i.e., the "like attracts like" phenomenon) and fail to learn discriminative embedding for anomalies that connect vast normal nodes. Moreover, such approaches identify anomalies in a unified global perspective but overlook diversified abnormal patterns conditioned on local graph context, leading to suboptimal performance. To overcome the aforementioned limitations, in this paper, we propose a Multi-hypersphere Heterophilic Graph Learning (MHetGL) framework for unsupervised GAD. Specifically, we first devise a Heterophilic Graph Encoding (HGE) module to learn distinguishable representations for potential anomalies by purifying and augmenting their neighborhood in a fully unsupervised manner. Then, we propose a Multi-Hypersphere Learning (MHL) module to enhance the detection capability for context-dependent anomalies by jointly incorporating critical patterns from both global and local perspectives. Extensive experiments on ten real-world datasets show that MHetGL outperforms 14 baselines. Our code is publicly available at https://github.com/KennyNH/MHetGL.