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Support Vector Machines in the Hilbert Geometry

Authors Aditya Acharya , Auguste H. Gezalyan , Julian Vanecek, David M. Mount , Sunil Arya

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Support vector machines
  • Hilbert geometry
  • linear classification
  • machine learning
  • LP-type problems

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Abstract

Support Vector Machines (SVMs) are a class of classification models in machine learning that are based on computing a maximum-margin separator between two sets of points. The SVM problem has been heavily studied for Euclidean geometry and for a number of kernels. In this paper, we consider the linear SVM problem in the Hilbert metric, a non-Euclidean geometry defined over a convex body. We present efficient algorithms for computing the SVM classifier for a set of n points in the Hilbert metric defined by convex polygons in the plane and convex polytopes in d-dimensional space. We also consider the problems in the related Funk distance.

Cite As Get BibTex

Aditya Acharya, Auguste H. Gezalyan, Julian Vanecek, David M. Mount, and Sunil Arya. Support Vector Machines in the Hilbert Geometry. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.3

Author Details

Aditya Acharya
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Auguste H. Gezalyan
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Julian Vanecek
  • Department of Computer Science, University of Maryland, College Park, MD, USA
David M. Mount
  • Department of Computer Science, University of Maryland, College Park, MD, USA
Sunil Arya
  • Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong

Funding

  • Arya, Sunil: Research Grants Council of Hong Kong, China project number 16214721.

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