Support Vector Machines and Radon's Theorem

A support vector machine (SVM) is an algorithm which finds a hyperplane that optimally separates labeled data points in R^n into positive and negative classes. The data points on the margin of this separating hyperplane are called support vectors. We connect the possible configurations of support vectors to Radon?s theorem, which provides guarantees for when a set of points can be divided into two classes (positive and negative) whose convex hulls intersect. For example, if the convex hulls of the positive and negative support vectors are projected onto a separating hyperplane, then the projections intersect if and only if the hyperplane is optimal. Joint work with Elin Farnell and Brittany Story. Accompanying paper: https://arxiv.org/abs/2011.00617 Talks slides: https://www.math.colostate.edu/~adams/talks/SVM-Radon.pdf