# Tverberg's theorem and multi-class support vector machines

arXiv: https://arxiv.org/abs/2404.16724 · HTML: https://mlsanity.com/paper/2404.16724/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 21 references that are in the map.
- First posted on arXiv 25 Apr 2024.

## Builds on (most cited first, 1 of 1)

- [Support vector machines and Radon's theorem](https://mlsanity.com/paper/2011.00617/) (2020)

## Abstract (arXiv)

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.