Tverberg's theorem and multi-class support vector machines
This work addresses the challenge of multi-class classification in machine learning, offering a novel theoretical approach that is incremental in nature.
The paper tackles the problem of designing multi-class support vector machines (SVMs) by applying linear-algebraic tools from Tverberg's theorem in combinatorial geometry, resulting in models that require fewer classification conditions and can be computed using existing binary SVM algorithms in higher-dimensional spaces.
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.