Tverberg's theorem and multi-class support vector machines
<|reference_start|>Tverberg's theorem and multi-class support vector machines: 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.<|reference_end|>
@article{soberón2024tverberg's,
    title={Tverberg's theorem and multi-class support vector machines},
    author={Pablo Sober'on},
    journal={arXiv preprint arXiv:2404.16724},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16724},
    primaryClass={cs.LG}
}