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Deep Orthogonal Hypersphere Compression for Anomaly Detection
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Proposes DOHSC (hypersphere contraction with an SVD-based orthogonal projection layer) and DO2HSC (bi-hypersphere shell decision region), plus graph-level extensions using GIN with mutual-information maximization, for one-class anomaly detection.
Problem
Hypersphere-based deep anomaly detection yields non-spherical decision boundaries, and in high dimensions normal data concentrate away from the center (soap-bubble effect) and the single hypersphere is sparse and incompact, raising false negatives.
Approach
An SVD-based orthogonal projection layer makes latent features decorrelated and standardized so the learned boundary matches a hypersphere; a co-centered bi-hypersphere (shell) decision region replaces the single ball to address the soap-bubble effect and compactness, with a new score function.
Key results
- DO2HSC reaches 0.98 ± 0.59 F1 on Thyroid vs 0.77 for PLAD, and 0.74 ± 0.02 F1 on Arrhythmia vs 0.71 for PLAD.
- On CIFAR-10, DOHSC and DO2HSC surpass prior SOTA in most classes, e.g., DO2HSC 84.4 AUC on ship vs 80.6 for PLAD.
- On graph-level benchmarks, DO2HSC achieves best AUC on all reported datasets, e.g., 0.9390 on COLLAB class 0 vs 0.6504 for OCGTL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the single hypersphere with a bi-hypersphere interval | DOHSC · CIFAR-10 Ship | AUC: 83.3 -> 84.4 | Helped |
| Replace the single hypersphere with a bi-hypersphere interval | DOHSC · CIFAR-10 Frog | AUC: 83.1 -> 83.0 | Hurt |
| Replace the single hypersphere with a bi-hypersphere interval | DOHSC · Thyroid | F1-score: 0.92 ± 0.01 -> 0.98 ± 0.59 | Helped |
| Replace the single hypersphere with a bi-hypersphere interval | DOHSC · Arrhythmia | F1-score: 0.70 ± 0.03 -> 0.74 ± 0.02 | Helped |
| Replace the single hypersphere with a bi-hypersphere interval | Graph-level DOHSC · ER_MD class 1 | AUC: 0.5184 ± 0.0793 -> 0.7351 ± 0.0159 | Helped |
Surprising findings
- Reports that a fixed or two-stage representation leaves many instances near the decision boundary, and that normal data in high dimensions concentrate away from the center (soap-bubble effect).
Limitations
- Does not consider training data with multiple normal classes (multi-class normal data).
- Hyperparameters such as the percentile nu and projection dimension require selection; experiments use test-time tuning of nu over a grid.
- Some graph baselines ran out of memory (RW on COLLAB and DD), and results on some classes are mixed, e.g., DOHSC underperforms on ER_MD class 1.
Experimental setup
Datasets: CIFAR-10 Fashion-MNIST Thyroid Arrhythmia COLLAB COX2 ER_MD MUTAG DD IMDB-Binary
Benchmarks: CIFAR-10 Fashion-MNIST Thyroid Arrhythmia COLLAB MUTAG ER_MD COX2 DD IMDB-Binary
Metrics: AUC F1-score
Baselines: Deep SVDD OCGAN DROCC HRN PLAD OCSVM LOF GOAD OCGIN infoGraph+Deep SVDD GLocalKD OCGTL
Builds on: Deep SVDD SVDD PCA Graph Isomorphism Network Jensen-Shannon mutual information estimator
Closest papers by meaning
- Hyperbolic Anomaly Detection (CVPR 2024 · similarity 0.86)
- Distribution Prototype Diffusion Learning for Open-set Supervised Anomaly Detection (CVPR 2025 · similarity 0.84)
- DiffGAD: A Diffusion-based Unsupervised Graph Anomaly Detector (ICLR 2025 · similarity 0.84)
- Towards a Unified Framework of Clustering-based Anomaly Detection (ICML 2025 · similarity 0.83)
- ResAD: A Simple Framework for Class Generalizable Anomaly Detection (NeurIPS 2024 · similarity 0.83)
- Unifying Unsupervised Graph-Level Anomaly Detection and Out-of-Distribution Detection: A Benchmark (ICLR 2025 · similarity 0.83)
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