Tverberg's theorem and multi-class support vector machines

TL;DR

This paper introduces new multi-class support vector machine models based on Tverberg's theorem, requiring fewer conditions for classification and leveraging existing binary SVM algorithms, with theoretical guarantees and geometric insights.

Contribution

It applies combinatorial geometry tools to develop novel multi-class SVM models with simplified conditions and proven theoretical properties.

Findings

New multi-class SVM models derived from Tverberg's theorem

Models can be computed using existing binary SVM algorithms

Theoretical guarantees of standard SVMs extend to these new models

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.