Support vector machines and Radon's theorem

A support vector machine (SVM) is an algorithm that finds a hyperplane which optimally separates labeled data points in \begin{document}$ \mathbb{R}^n $\end{document} into positive and negative classes. The on the margin of this separating are called support vectors. We connect possible configurations vectors to Radon's theorem, provides guarantees for when set can be divided two classes (positive negative) whose convex hulls intersect. If projected onto hyperplane, then projections intersect if only optimal. Further, with particular type general position, we show (a) exactly one point, (b) stable under perturbation, (c) there at most id="M2">\begin{document}$ n+1 vectors, (d) every number from 2 up id="M3">\begin{document}$ possible. Finally, perform computer simulations studying expected their configurations, randomly generated data. observe as distance between increases data, fewer become more likely.