Comparing Euclidean and Hyperbolic K-Means for Generalized Category Discovery

2026-02-04

AI Summary

This work addresses a key limitation in existing generalized category discovery (GCD) methods, which typically perform clustering in Euclidean space despite learning representations on hyperspheres, thereby failing to exploit the inherent hierarchical structure of data. To overcome this, we propose HC-GCD, the first end-to-end framework for GCD that operates entirely in hyperbolic space. Our approach leverages the Lorentz model to learn hyperbolic embeddings and directly applies hyperbolic K-Means for clustering, eliminating the need for any projection into Euclidean space. Evaluated on the Semantic Shift Benchmark, HC-GCD achieves state-of-the-art performance, significantly improving clustering accuracy for unseen categories and demonstrating enhanced robustness to variations in label granularity.

Technology Category

• Machine Learning: Clustering
• Search and Optimization: Mixed Discrete/Continuous Search
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text

Abstract

Hyperbolic representation learning has been widely used to extract implicit hierarchies within data, and recently it has found its way to the open-world classification task of Generalized Category Discovery (GCD). However, prior hyperbolic GCD methods only use hyperbolic geometry for representation learning and transform back to Euclidean geometry when clustering. We hypothesize this is suboptimal. Therefore, we present Hyperbolic Clustered GCD (HC-GCD), which learns embeddings in the Lorentz Hyperboloid model of hyperbolic geometry, and clusters these embeddings directly in hyperbolic space using a hyperbolic K-Means algorithm. We test our model on the Semantic Shift Benchmark datasets, and demonstrate that HC-GCD is on par with the previous state-of-the-art hyperbolic GCD method. Furthermore, we show that using hyperbolic K-Means leads to better accuracy than Euclidean K-Means. We carry out ablation studies showing that clipping the norm of the Euclidean embeddings leads to decreased accuracy in clustering unseen classes, and increased accuracy for seen classes, while the overall accuracy is dataset dependent. We also show that using hyperbolic K-Means leads to more consistent clusters when varying the label granularity.

Problem

• Generalized Category Discovery
• Hyperbolic Geometry
• K-Means Clustering
• Representation Learning
• Open-World Classification

Innovation

• Hyperbolic K-Means
• Generalized Category Discovery
• Lorentz Hyperboloid Model
• Hyperbolic Representation Learning
• Open-World Classification