# Self-Discriminative Modeling for Anomalous Graph Detection

arXiv: https://arxiv.org/abs/2310.06261 · HTML: https://mlsanity.com/paper/2310.06261/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [A Unifying Review of Deep and Shallow Anomaly Detection](https://mlsanity.com/paper/2009.11732/) (2020)
- [Provably Powerful Graph Networks](https://mlsanity.com/paper/1905.11136/) (2019)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [graph2vec: Learning Distributed Representations of Graphs](https://mlsanity.com/paper/1707.05005/) (2017)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Neural Transformation Learning for Deep Anomaly Detection Beyond Images](https://mlsanity.com/paper/2103.16440/) (2021)
- [Generative and Contrastive Self-Supervised Learning for Graph Anomaly Detection](https://mlsanity.com/paper/2108.09896/) (2021)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [On Using Classification Datasets to Evaluate Graph-Level Outlier Detection: Peculiar Observations and New Insights](https://mlsanity.com/paper/2012.12931/) (2020)
- [Raising the Bar in Graph-level Anomaly Detection](https://mlsanity.com/paper/2205.13845/) (2022)
- [word2vec, node2vec, graph2vec, X2vec: Towards a Theory of Vector Embeddings of Structured Data](https://mlsanity.com/paper/2003.12590/) (2020)
- [Second-Order Pooling for Graph Neural Networks](https://mlsanity.com/paper/2007.10467/) (2020)

## Built on by (most cited first, 6 of 6)

- [Deep Graph Anomaly Detection: A Survey and New Perspectives](https://mlsanity.com/paper/2409.09957/) (2024)
- [Generative Semi-supervised Graph Anomaly Detection](https://mlsanity.com/paper/2402.11887/) (2024)
- [Subject Information Extraction for Novelty Detection with Domain Shifts](https://mlsanity.com/paper/2504.21247/) (2025)
- [Learnable Kernel Density Estimation for Graphs and Its Application to Graph-Level Anomaly Detection](https://mlsanity.com/paper/2505.21285/) (2025)
- [Fairness-aware Anomaly Detection via Fair Projection](https://mlsanity.com/paper/2505.11132/) (2025)
- [UniOD: A Universal Model for Outlier Detection across Diverse Domains](https://mlsanity.com/paper/2507.06624/) (2025)

## Abstract (arXiv)

This paper studies the problem of detecting anomalous graphs using a machine learning model trained on only normal graphs, which has many applications in molecule, biology, and social network data analysis. We present a self-discriminative modeling framework for anomalous graph detection. The key idea, mathematically and numerically illustrated, is to learn a discriminator (classifier) from the given normal graphs together with pseudo-anomalous graphs generated by a model jointly trained, where we never use any true anomalous graphs and we hope that the generated pseudo-anomalous graphs interpolate between normal ones and (real) anomalous ones. Under the framework, we provide three algorithms with different computational efficiencies and stabilities for anomalous graph detection. The three algorithms are compared with several state-of-the-art graph-level anomaly detection baselines on nine popular graph datasets (four with small size and five with moderate size) and show significant improvement in terms of AUC. The success of our algorithms stems from the integration of the discriminative classifier and the well-posed pseudo-anomalous graphs, which provide new insights for anomaly detection. Moreover, we investigate our algorithms for large-scale imbalanced graph datasets. Surprisingly, our algorithms, though fully unsupervised, are able to significantly outperform supervised learning algorithms of anomalous graph detection. The corresponding reason is also analyzed.