# Deep Orthogonal Hypersphere Compression for Anomaly Detection

arXiv: https://arxiv.org/abs/2302.06430 · HTML: https://mlsanity.com/paper/2302.06430/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 13 Feb 2023.

## Builds on (most cited first, 21 of 21)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [InfoGraph: Unsupervised and Semi-supervised Graph-Level Representation Learning via Mutual Information Maximization](https://mlsanity.com/paper/1908.01000/) (2019)
- [Deep Semi-Supervised Anomaly Detection](https://mlsanity.com/paper/1906.02694/) (2019)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [OCGAN: One-class Novelty Detection Using GANs with Constrained Latent Representations](https://mlsanity.com/paper/1903.08550/) (2019)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [Learning and Evaluating Representations for Deep One-class Classification](https://mlsanity.com/paper/2011.02578/) (2020)
- [Explainable Deep One-Class Classification](https://mlsanity.com/paper/2007.01760/) (2020)
- [DROCC: Deep Robust One-Class Classification](https://mlsanity.com/paper/2002.12718/) (2020)
- [Deep One-Class Classification via Interpolated Gaussian Descriptor](https://mlsanity.com/paper/2101.10043/) (2021)
- [Deep Graph-level Anomaly Detection by Glocal Knowledge Distillation](https://mlsanity.com/paper/2112.10063/) (2021)
- [GraKeL: A Graph Kernel Library in Python](https://mlsanity.com/paper/1806.02193/) (2018)
- [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)
- [Explainable Classification of Brain Networks via Contrast Subgraphs](https://mlsanity.com/paper/2006.05176/) (2020)
- [Perturbation Learning Based Anomaly Detection](https://mlsanity.com/paper/2206.02704/) (2022)
- [Exactly Robust Kernel Principal Component Analysis](https://mlsanity.com/paper/1802.10558/) (2018)

## Built on by (most cited first, 12 of 12)

- [ARC: A Generalist Graph Anomaly Detector with In-Context Learning](https://mlsanity.com/paper/2405.16771/) (2024)
- [A Label-Free Heterophily-Guided Approach for Unsupervised Graph Fraud Detection](https://mlsanity.com/paper/2502.13308/) (2025)
- [Subject Information Extraction for Novelty Detection with Domain Shifts](https://mlsanity.com/paper/2504.21247/) (2025)
- [Removing Geometric Bias in One-Class Anomaly Detection with Adaptive Feature Perturbation](https://mlsanity.com/paper/2503.05520/) (2025)
- [ResAD++: Towards Class Agnostic Anomaly Detection via Residual Feature Learning](https://mlsanity.com/paper/2509.23741/) (2025)
- [Interpretable Maximum Margin Deep Anomaly Detection](https://mlsanity.com/paper/2603.07073/) (2026)
- [LTCR: Long-Text Chinese Rumor Detection Dataset](https://mlsanity.com/paper/2306.07201/) (2023)
- [Fairness-aware Anomaly Detection via Fair Projection](https://mlsanity.com/paper/2505.11132/) (2025)
- [Time-reversed Flow Matching with Worst Transport in High-dimensional Latent Space for Image Anomaly Detection](https://mlsanity.com/paper/2508.05461/) (2025)
- [UniOD: A Universal Model for Outlier Detection across Diverse Domains](https://mlsanity.com/paper/2507.06624/) (2025)
- [Why the Counterintuitive Phenomenon of Likelihood Rarely Appears in Tabular Anomaly Detection with Deep Generative Models?](https://mlsanity.com/paper/2602.09593/) (2026)
- [Learning Discriminative and Generalizable Anomaly Detector for Dynamic Graph with Limited Supervision](https://mlsanity.com/paper/2602.20019/) (2026)

## Abstract (arXiv)

Many well-known and effective anomaly detection methods assume that a reasonable decision boundary has a hypersphere shape, which however is difficult to obtain in practice and is not sufficiently compact, especially when the data are in high-dimensional spaces. In this paper, we first propose a novel deep anomaly detection model that improves the original hypersphere learning through an orthogonal projection layer, which ensures that the training data distribution is consistent with the hypersphere hypothesis, thereby increasing the true positive rate and decreasing the false negative rate. Moreover, we propose a bi-hypersphere compression method to obtain a hyperspherical shell that yields a more compact decision region than a hyperball, which is demonstrated theoretically and numerically. The proposed methods are not confined to common datasets such as image and tabular data, but are also extended to a more challenging but promising scenario, graph-level anomaly detection, which learns graph representation with maximum mutual information between the substructure and global structure features while exploring orthogonal single- or bi-hypersphere anomaly decision boundaries. The numerical and visualization results on benchmark datasets demonstrate the superiority of our methods in comparison to many baselines and state-of-the-art methods.