Tverberg's theorem and multi-class support vector machines

• URL: http://arxiv.org/abs/2404.16724v1
• Date: Thu, 25 Apr 2024 16:37:58 GMT
• Title: Tverberg's theorem and multi-class support vector machines
• Authors: Pablo Soberón,
• Abstract summary: We show how we can design new models of multi-class support vector machines (SVMs) These protocols require fewer conditions to classify sets of points, and can be computed using existing binary SVM algorithms in higher-dimensional spaces. We give a new simple proof of a geometric characterization of support vectors for largest margin SVMs by Veelaert.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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