2026-07-26T16:24:43Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24234 2025-11-12T13:39:13Z ddc:004 open_access

Support Vector Machines in the Hilbert Geometry Acharya, Aditya Gezalyan, Auguste H. Vanecek, Julian Mount, David M. Arya, Sunil Support vector machines Hilbert geometry linear classification machine learning LP-type problems 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Aditya Acharya and Auguste H. Gezalyan and Julian Vanecek and David M. Mount and Sunil Arya 2025 Is Part Of LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.WADS.2025.3 urn:nbn:de:0030-drops-242348 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.3 eng https://creativecommons.org/licenses/by/4.0/legalcode