# Comparing Euclidean and Hyperbolic K-Means for Generalized Category Discovery

arXiv: https://arxiv.org/abs/2602.04932 · HTML: https://mlsanity.com/paper/2602.04932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 27 of 27)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Generalized Category Discovery](https://mlsanity.com/paper/2201.02609/) (2022)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Parametric Classification for Generalized Category Discovery: A Baseline Study](https://mlsanity.com/paper/2211.11727/) (2022)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Learning Semi-supervised Gaussian Mixture Models for Generalized Category Discovery](https://mlsanity.com/paper/2305.06144/) (2023)
- [Hyperbolic Contrastive Learning for Visual Representations beyond Objects](https://mlsanity.com/paper/2212.00653/) (2022)
- [No Representation Rules Them All in Category Discovery](https://mlsanity.com/paper/2311.17055/) (2023)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [SPTNet: An Efficient Alternative Framework for Generalized Category Discovery with Spatial Prompt Tuning](https://mlsanity.com/paper/2403.13684/) (2024)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Learn to Categorize or Categorize to Learn? Self-Coding for Generalized Category Discovery](https://mlsanity.com/paper/2310.19776/) (2023)
- [SelEx: Self-Expertise in Fine-Grained Generalized Category Discovery](https://mlsanity.com/paper/2408.14371/) (2024)
- [Capturing implicit hierarchical structure in 3D biomedical images with self-supervised hyperbolic representations](https://mlsanity.com/paper/2012.01644/) (2020)
- [Skip-gram word embeddings in hyperbolic space](https://mlsanity.com/paper/1809.01498/) (2018)
- [Hyperbolic Category Discovery](https://mlsanity.com/paper/2504.06120/) (2025)
- [SEAL: Semantic-Aware Hierarchical Learning for Generalized Category Discovery](https://mlsanity.com/paper/2510.18740/) (2025)
- [Klein Model for Hyperbolic Neural Networks](https://mlsanity.com/paper/2410.16813/) (2024)
- [HIDISC: A Hyperbolic Framework for Domain Generalization with Generalized Category Discovery](https://mlsanity.com/paper/2510.17188/) (2025)

## Abstract (arXiv)

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.