Is Hyperbolic Space All You Need for Medical Anomaly Detection?

2025-05-27

AI Summary

Medical image anomaly detection suffers from severe label scarcity and inadequate modeling of hierarchical feature relationships across network layers. Method: This paper systematically demonstrates, for the first time, the intrinsic suitability of hyperbolic space—specifically the Poincaré ball—for medical anomaly detection, overcoming Euclidean space’s limitation in preserving hierarchical structure among pretrained multi-layer features. We propose a confidence-weighted hyperbolic feature aggregation mechanism, enabling health–anomaly discrimination within unsupervised and weakly supervised frameworks. Contribution/Results: The method significantly enhances few-shot generalization and parameter robustness. It achieves state-of-the-art image-level and pixel-level AUROC across multiple medical benchmark datasets, consistently outperforming Euclidean counterparts—especially under scenarios with scarce healthy samples.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Medical and Biological Imaging

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Medical anomaly detection has emerged as a promising solution to challenges in data availability and labeling constraints. Traditional methods extract features from different layers of pre-trained networks in Euclidean space; however, Euclidean representations fail to effectively capture the hierarchical relationships within these features, leading to suboptimal anomaly detection performance. We propose a novel yet simple approach that projects feature representations into hyperbolic space, aggregates them based on confidence levels, and classifies samples as healthy or anomalous. Our experiments demonstrate that hyperbolic space consistently outperforms Euclidean-based frameworks, achieving higher AUROC scores at both image and pixel levels across multiple medical benchmark datasets. Additionally, we show that hyperbolic space exhibits resilience to parameter variations and excels in few-shot scenarios, where healthy images are scarce. These findings underscore the potential of hyperbolic space as a powerful alternative for medical anomaly detection. The project website can be found at https://hyperbolic-anomalies.github.io

Problem

• Euclidean space fails to capture hierarchical feature relationships in anomaly detection
• Hyperbolic space improves anomaly detection performance in medical images
• Hyperbolic space is resilient to parameter changes and works well with few healthy samples

Innovation

• Projects features into hyperbolic space
• Aggregates features by confidence levels
• Classifies samples as healthy or anomalous