# Large-Margin Classification in Hyperbolic Space

arXiv: https://arxiv.org/abs/1806.00437 · HTML: https://mlsanity.com/paper/1806.00437/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2018.

## Built on by (most cited first, 30 of 41)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [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)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [The Numerical Stability of Hyperbolic Representation Learning](https://mlsanity.com/paper/2211.00181/) (2022)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [HyperMiner: Topic Taxonomy Mining with Hyperbolic Embedding](https://mlsanity.com/paper/2210.10625/) (2022)
- [Generalization Error Bound for Hyperbolic Ordinal Embedding](https://mlsanity.com/paper/2105.10475/) (2021)
- [Linear Classifiers in Product Space Forms](https://mlsanity.com/paper/2102.10204/) (2021)
- [Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space](https://mlsanity.com/paper/2302.06807/) (2023)
- [Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classification](https://mlsanity.com/paper/2306.14822/) (2023)
- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)
- [Highly Scalable and Provably Accurate Classification in Poincare Balls](https://mlsanity.com/paper/2109.03781/) (2021)
- [Random Laplacian Features for Learning with Hyperbolic Space](https://mlsanity.com/paper/2202.06854/) (2022)
- [HyperFed: Hyperbolic Prototypes Exploration with Consistent Aggregation for Non-IID Data in Federated Learning](https://mlsanity.com/paper/2307.14384/) (2023)
- [Hyperbolic Space with Hierarchical Margin Boosts Fine-Grained Learning from Coarse Labels](https://mlsanity.com/paper/2311.11019/) (2023)
- [Fast hyperboloid decision tree algorithms](https://mlsanity.com/paper/2310.13841/) (2023)
- [Klein Model for Hyperbolic Neural Networks](https://mlsanity.com/paper/2410.16813/) (2024)
- [Continual Hyperbolic Learning of Instances and Classes](https://mlsanity.com/paper/2506.10710/) (2025)
- [Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networks](https://mlsanity.com/paper/2405.15481/) (2024)
- [Augmenting the User-Item Graph with Textual Similarity Models](https://mlsanity.com/paper/2109.09358/) (2021)
- [HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clustering](https://mlsanity.com/paper/2205.09721/) (2022)
- [Geometric Learning with Positively Decomposable Kernels](https://mlsanity.com/paper/2310.13821/) (2023)
- [Adversarial Attacks on Hyperbolic Networks](https://mlsanity.com/paper/2412.01495/) (2024)
- [Provably Accurate and Scalable Linear Classifiers in Hyperbolic Spaces](https://mlsanity.com/paper/2203.03730/) (2022)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2407.16641/) (2024)

## Abstract (arXiv)

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. With the goal of enabling accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce hyperbolic SVM, a hyperbolic formulation of support vector machine classifiers, and elucidate through new theoretical work its connection to the Euclidean counterpart. We demonstrate the performance improvement of hyperbolic SVM for multi-class prediction tasks on real-world complex networks as well as simulated datasets. Our work allows analytic pipelines that take the inherent hyperbolic geometry of the data into account in an end-to-end fashion without resorting to ill-fitting tools developed for Euclidean space.