# Graph Regularized Autoencoder and its Application in Unsupervised Anomaly Detection

arXiv: https://arxiv.org/abs/2010.15949 · HTML: https://mlsanity.com/paper/2010.15949/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 11 of 11)

- [A Comprehensive Survey on Deep Graph Representation Learning](https://mlsanity.com/paper/2304.05055/) (2023)
- [A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and Open Resource](https://mlsanity.com/paper/2211.12875/) (2022)
- [Graph Anomaly Detection in Time Series: A Survey](https://mlsanity.com/paper/2302.00058/) (2023)
- [A Survey of Imbalanced Learning on Graphs: Problems, Techniques, and Future Directions](https://mlsanity.com/paper/2308.13821/) (2023)
- [Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions](https://mlsanity.com/paper/2401.02143/) (2024)
- [Homophily-enhanced Structure Learning for Graph Clustering](https://mlsanity.com/paper/2308.05309/) (2023)
- [From Few-Shot to Zero-Shot: Towards Generalist Graph Anomaly Detection](https://mlsanity.com/paper/2602.18793/) (2026)
- [Few-Shot Anomaly Detection via Category-Agnostic Registration Learning](https://mlsanity.com/paper/2406.08810/) (2024)
- [Learning a Cross-modality Anomaly Detector for Remote Sensing Imagery](https://mlsanity.com/paper/2310.07511/) (2023)
- [Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization](https://mlsanity.com/paper/2112.04193/) (2021)
- [AD-NEv++ : The multi-architecture neuroevolution-based multivariate anomaly detection framework](https://mlsanity.com/paper/2404.07968/) (2024)

## Abstract (arXiv)

Dimensionality reduction is a crucial first step for many unsupervised learning tasks including anomaly detection and clustering. Autoencoder is a popular mechanism to accomplish dimensionality reduction. In order to make dimensionality reduction effective for high-dimensional data embedding nonlinear low-dimensional manifold, it is understood that some sort of geodesic distance metric should be used to discriminate the data samples. Inspired by the success of geodesic distance approximators such as ISOMAP, we propose to use a minimum spanning tree (MST), a graph-based algorithm, to approximate the local neighborhood structure and generate structure-preserving distances among data points. We use this MST-based distance metric to replace the Euclidean distance metric in the embedding function of autoencoders and develop a new graph regularized autoencoder, which outperforms a wide range of alternative methods over 20 benchmark anomaly detection datasets. We further incorporate the MST regularizer into two generative adversarial networks and find that using the MST regularizer improves the performance of anomaly detection substantially for both generative adversarial networks. We also test our MST regularized autoencoder on two datasets in a clustering application and witness its superior performance as well.