# Rethinking Graph Neural Networks for Anomaly Detection

arXiv: https://arxiv.org/abs/2205.15508 · HTML: https://mlsanity.com/paper/2205.15508/

## Key facts

- Cited by 187 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 58 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [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)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Revisiting Graph Neural Networks: All We Have is Low-Pass Filters](https://mlsanity.com/paper/1905.09550/) (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)
- [CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters](https://mlsanity.com/paper/1705.07664/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [A Semi-supervised Graph Attentive Network for Financial Fraud Detection](https://mlsanity.com/paper/2003.01171/) (2020)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews](https://mlsanity.com/paper/1303.4402/) (2013)
- [Learning Structural Node Embeddings Via Diffusion Wavelets](https://mlsanity.com/paper/1710.10321/) (2017)
- [Alleviating the Inconsistency Problem of Applying Graph Neural Network to Fraud Detection](https://mlsanity.com/paper/2005.00625/) (2020)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [AdaGNN: Graph Neural Networks with Adaptive Frequency Response Filter](https://mlsanity.com/paper/2104.12840/) (2021)
- [Outlier Aware Network Embedding for Attributed Networks](https://mlsanity.com/paper/1811.07609/) (2018)
- [Interpretable, Multidimensional, Multimodal Anomaly Detection with Negative Sampling for Detection of Device Failure](https://mlsanity.com/paper/2007.10088/) (2020)
- [Deconvolutional Networks on Graph Data](https://mlsanity.com/paper/2110.15528/) (2021)
- [Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering](https://mlsanity.com/paper/2107.04755/) (2021)
- [Geometric Scattering Attention Networks](https://mlsanity.com/paper/2010.15010/) (2020)
- [Compactly Supported One-cyclic Wavelets Derived from Beta Distributions](https://mlsanity.com/paper/1502.02166/) (2015)

## Built on by (most cited first, 30 of 187)

- [All in One: Multi-task Prompting for Graph Neural Networks](https://mlsanity.com/paper/2307.01504/) (2023)
- [All in One and One for All: A Simple yet Effective Method towards Cross-domain Graph Pretraining](https://mlsanity.com/paper/2402.09834/) (2024)
- [ZeroG: Investigating Cross-dataset Zero-shot Transferability in Graphs](https://mlsanity.com/paper/2402.11235/) (2024)
- [Energy Transformer](https://mlsanity.com/paper/2302.07253/) (2023)
- [Parameter-Efficient Fine-Tuning with Discrete Fourier Transform](https://mlsanity.com/paper/2405.03003/) (2024)
- [GADBench: Revisiting and Benchmarking Supervised Graph Anomaly Detection](https://mlsanity.com/paper/2306.12251/) (2023)
- [Graph Anomaly Detection via Multi-Scale Contrastive Learning Networks with Augmented View](https://mlsanity.com/paper/2212.00535/) (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)
- [GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction](https://mlsanity.com/paper/2306.01951/) (2023)
- [Does Graph Distillation See Like Vision Dataset Counterpart?](https://mlsanity.com/paper/2310.09192/) (2023)
- [Truncated Affinity Maximization: One-class Homophily Modeling for Graph Anomaly Detection](https://mlsanity.com/paper/2306.00006/) (2023)
- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Alleviating Structural Distribution Shift in Graph Anomaly Detection](https://mlsanity.com/paper/2401.14155/) (2024)
- [Inductive Graph Unlearning](https://mlsanity.com/paper/2304.03093/) (2023)
- [ProG: A Graph Prompt Learning Benchmark](https://mlsanity.com/paper/2406.05346/) (2024)
- [Zero-shot Generalist Graph Anomaly Detection with Unified Neighborhood Prompts](https://mlsanity.com/paper/2410.14886/) (2024)
- [SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases](https://mlsanity.com/paper/2308.13212/) (2023)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [ADA-GAD: Anomaly-Denoised Autoencoders for Graph Anomaly Detection](https://mlsanity.com/paper/2312.14535/) (2023)
- [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)
- [Revisiting Graph-Based Fraud Detection in Sight of Heterophily and Spectrum](https://mlsanity.com/paper/2312.06441/) (2023)
- [Rayleigh Quotient Graph Neural Networks for Graph-level Anomaly Detection](https://mlsanity.com/paper/2310.02861/) (2023)
- [Breaking the Entanglement of Homophily and Heterophily in Semi-supervised Node Classification](https://mlsanity.com/paper/2312.04111/) (2023)
- [Anomaly Detection in Dynamic Graphs: A Comprehensive Survey](https://mlsanity.com/paper/2406.00134/) (2024)
- [Alleviating Over-smoothing for Unsupervised Sentence Representation](https://mlsanity.com/paper/2305.06154/) (2023)
- [A Fused Gromov-Wasserstein Framework for Unsupervised Knowledge Graph Entity Alignment](https://mlsanity.com/paper/2305.06574/) (2023)
- [Semi-Supervised Hierarchical Graph Classification](https://mlsanity.com/paper/2206.05416/) (2022)
- [Robust Attributed Graph Alignment via Joint Structure Learning and Optimal Transport](https://mlsanity.com/paper/2301.12721/) (2023)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are widely applied for graph anomaly detection. As one of the key components for GNN design is to select a tailored spectral filter, we take the first step towards analyzing anomalies via the lens of the graph spectrum. Our crucial observation is the existence of anomalies will lead to the `right-shift' phenomenon, that is, the spectral energy distribution concentrates less on low frequencies and more on high frequencies. This fact motivates us to propose the Beta Wavelet Graph Neural Network (BWGNN). Indeed, BWGNN has spectral and spatial localized band-pass filters to better handle the `right-shift' phenomenon in anomalies. We demonstrate the effectiveness of BWGNN on four large-scale anomaly detection datasets. Our code and data are released at https://github.com/squareRoot3/Rethinking-Anomaly-Detection