Work

Tverberg's theorem and multi-class support vector machines

Year: 2024

Type: article

Abstract: We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions to classify sets of points, and can be computed using existing binary SVM algorithms in higher-dimensional spaces, including soft-margin SVM algorithms. We describe how the theoretical guarantees of standard support vector machines transfer to these new classes of multi-class support vector machines. We give a new simple proof of a geometric characterization of support vectors for largest margin SVMs by Veelaert.

Source: Foundations of Data Science

DOI: 10.3934/fods.2024039

Author: Pablo Soberón

Language: English

Topic: Machine Learning and Algorithms

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, City University of New York

Awards: CAREER: Discrete Geometry at the crossroads of Combinatorics and Topology, G6671297155, Topology and Linear Algebra in Discrete Geometry

OpenAlex ID: W4402416417

FWCI: 0.148

Cites: 21

Cited by: 1

Related to: 10