mlsanityData to 7 Oct 2026

Large-Margin Classification in Hyperbolic Space

arXiv 1806.00437 ↗First posted 1 Jun 2018cs.LG stat.MLcited by 41

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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.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jun 2018.

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Citing papers per year: 2021: 10; 2022: 7; 2023: 11; 2024: 8; 2025: 4; 2026: 1.

41 papers.

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  1. 2021Hyperbolic Deep Neural Networks: A Surveycited by 138
  2. 2022Hyperbolic Image Segmentationcited by 101
  3. 2023Hyperbolic Deep Learning in Computer Vision: A Surveycited by 72
  4. 2021Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifierscited by 56
  5. 2023Fully Hyperbolic Convolutional Neural Networks for Computer Visioncited by 48
  6. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  7. 2022The Numerical Stability of Hyperbolic Representation Learningcited by 46
  8. 2021Hyperbolic Busemann Learning with Ideal Prototypescited by 40
  9. 2021CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Datacited by 28
  10. 2022HyperMiner: Topic Taxonomy Mining with Hyperbolic Embeddingcited by 15
  11. 2021Generalization Error Bound for Hyperbolic Ordinal Embeddingcited by 12
  12. 2021Linear Classifiers in Product Space Formscited by 11
29 more
  1. 2023Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Spacecited by 11
  2. 2023Hyperbolic Random Forestscited by 9
  3. 2021Highly Scalable and Provably Accurate Classification in Poincare Ballscited by 8
  4. 2022Random Laplacian Features for Learning with Hyperbolic Spacecited by 8
  5. 2023Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classificationcited by 8
  6. 2023HyperFed: Hyperbolic Prototypes Exploration with Consistent Aggregation for Non-IID Data in Federated Learningcited by 8
  7. 2023Hyperbolic Space with Hierarchical Margin Boosts Fine-Grained Learning from Coarse Labelscited by 8
  8. 2023Fast hyperboloid decision tree algorithmscited by 7
  9. 2024Sparse Spectral Training and Inference on Euclidean and Hyperbolic Neural Networkscited by 4
  10. 2025Continual Hyperbolic Learning of Instances and Classescited by 4
  11. 2021Augmenting the User-Item Graph with Textual Similarity Modelscited by 3
  12. 2022HyperAid: Denoising in hyperbolic spaces for tree-fitting and hierarchical clusteringcited by 3
  13. 2023Geometric Learning with Positively Decomposable Kernelscited by 3
  14. 2024Klein Model for Hyperbolic Neural Networkscited by 3
  15. 2024Adversarial Attacks on Hyperbolic Networkscited by 3
  16. 2022Provably Accurate and Scalable Linear Classifiers in Hyperbolic Spacescited by 2
  17. 2023Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networkscited by 2
  18. 2024A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Spacecited by 2
  19. 2024Mixed-curvature decision trees and random forestscited by 2
  20. 2021Unit Ball Model for Embedding Hierarchical Structures in the Complex Hyperbolic Spacecited by 1
  21. 2022Hyperbolic Centroid Calculations for Text Classificationcited by 0
  22. 2023Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hullscited by 0
  23. 2024Convex Relaxation for Solving Large-Margin Classifiers in Hyperbolic Spacecited by 0
  24. 2024Mixed-Curvature Decision Trees and Random Forestscited by 0
  25. 2024Enhance Hyperbolic Representation Learning via Second-order Poolingcited by 0
  26. 2025Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approachcited by 0
  27. 2025Hyperbolic Structured Classification for Robust Single Positive Multi-label Learningcited by 0
  28. 2025Adaptive Hyperbolic Kernels: Modulated Embedding in de Branges-Rovnyak Spacescited by 0
  29. 2026Classifiers in High Dimensional Hilbert Metricscited by 0