Is Hyperbolic Space All You Need for Medical Anomaly Detection?

TL;DR

This paper introduces a hyperbolic space-based method for medical anomaly detection, which captures hierarchical feature relationships better than Euclidean space, leading to improved performance especially in few-shot scenarios.

Contribution

The paper presents a novel approach that projects features into hyperbolic space for anomaly detection, demonstrating superior results over traditional Euclidean methods across multiple datasets.

Findings

Hyperbolic space outperforms Euclidean space in AUROC scores.

The method is resilient to parameter variations.

It performs well in few-shot learning scenarios.

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