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Classifiers in High Dimensional Hilbert Metrics

Authors Aditya Acharya , Auguste H. Gezalyan , David M. Mount

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Support vector machines
  • Hilbert geometry
  • classification
  • machine learning

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Abstract

Classifying points in high-dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address the problem of classifying points in the d-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of the Cayley-Klein hyperbolic distance to arbitrary convex bodies and has a diverse range of applications in machine learning and convex geometry. We first present an efficient LP-based algorithm in the metric for the large-margin SVM problem. Our algorithm runs in time polynomial in the number of points, the number of bounding facets, and the dimension. This is a significant improvement over previous work, which either provides no theoretical guarantees on runtime or suffers from exponential runtime. We also consider the closely related Funk metric. Finally, we present efficient algorithms for the soft-margin SVM problem and nearest-neighbor-based classification in the Hilbert metric.

Cite As Get BibTex

Aditya Acharya, Auguste H. Gezalyan, and David M. Mount. Classifiers in High Dimensional Hilbert Metrics. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 1:1-1:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.1

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
David M. Mount
  • Department of Computer Science, University of Maryland, College Park, MD, USA

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