Support vector machines and Radon's theorem. (arXiv:2011.00617v2 [cs.LG] UPDATED)

A support vector machine (SVM) is an algorithm which finds a hyperplane that
optimally separates labeled data points in $\mathbb{R}^n$ 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. If the convex hulls of the positive and …

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