mlsanityData to 7 Oct 2026

Horospherical Decision Boundaries for Large Margin Classification in Hyperbolic Space

arXiv 2302.06807 ↗First posted 14 Feb 2023stat.ML cs.LGcited by 11

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Abstract (arXiv)

Hyperbolic spaces have been quite popular in the recent past for representing hierarchically organized data. Further, several classification algorithms for data in these spaces have been proposed in the literature. These algorithms mainly use either hyperplanes or geodesics for decision boundaries in a large margin classifiers setting leading to a non-convex optimization problem. In this paper, we propose a novel large margin classifier based on horospherical decision boundaries that leads to a geodesically convex optimization problem that can be optimized using any Riemannian gradient descent technique guaranteeing a globally optimal solution. We present several experiments depicting the competitive performance of our classifier in comparison to SOTA.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 20 of its 36 references that are in the map. First posted on arXiv 14 Feb 2023.

Builds on

20 of 36 references.

References · 20

  1. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  2. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  3. 2018Hyperbolic Neural Networkscited by 393
  4. 2018Representation Tradeoffs for Hyperbolic Embeddingscited by 204
  5. 2018Hyperbolic Entailment Cones for Learning Hierarchical Embeddingscited by 160
  6. 2018Poincar'e GloVe: Hyperbolic Word Embeddingscited by 155
  7. 2017Cooperative Game Theory Approaches for Network Partitioningcited by 134
  8. 2019Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoderscited by 111
  9. 2016Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiationcited by 93
  10. 2016First-order Methods for Geodesically Convex Optimizationcited by 92
  11. 2017Neural Embeddings of Graphs in Hyperbolic Spacecited by 58
  12. 2014Geodesic Exponential Kernels: When Curvature and Linearity Conflictcited by 47
8 more
  1. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
  2. 2018Large-Margin Classification in Hyperbolic Spacecited by 41
  3. 2020Robust Large-Margin Learning in Hyperbolic Spacecited by 21
  4. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  5. 2022Fully-Connected Network on Noncompact Symmetric Space and Ridgelet Transform based on Helgason-Fourier Analysiscited by 14
  6. 2021Riemannian conjugate gradient methods: General framework and specific algorithms with convergence analysescited by 12
  7. 2021Highly Scalable and Provably Accurate Classification in Poincare Ballscited by 8
  8. 2020Hyperbolic Manifold Regressioncited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 2; 2025: 2; 2026: 5.

11 papers.

  1. 2023Fast hyperboloid decision tree algorithmscited by 7
  2. 2026Neural Networks on Symmetric Spaces of Noncompact Typecited by 5
  3. 2026Intrinsic Lorentz Neural Networkcited by 3
  4. 2025Geometry-aware Distance Measure for Diverse Hierarchical Structures in Hyperbolic Spacescited by 2
  5. 2026Hyperbolic Busemann Neural Networkscited by 2
  6. 2023Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applicationscited by 1
  7. 2024Horoballs and the subgradient methodcited by 1
  8. 2024Hyperboloid GPLVM for Discovering Continuous Hierarchies via Nonparametric Estimationcited by 0
  9. 2025Even Faster Hyperbolic Random Forests: A Beltrami-Klein Wrapper Approachcited by 0
  10. 20261-Lipschitz Neural Networks on Hadamard Manifoldscited by 0
  11. 2026Rethinking the Fully Hyperbolic Vision Transformer in Polar Coordinatescited by 0