Generic support vector machines and Radon's theorem
Date
2019
Authors
Carr, Brittany M., author
Adams, Henry, advisor
Shipman, Patrick, committee member
Fremstad, Anders, committee member
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Abstract
A support vector machine, (SVM), is an algorithm which finds a hyperplane that optimally separates labeled data points in Rn into positive and negative classes. The data points on the margin of this separating hyperplane are called \emph{support vectors}. We study the possible configurations of support vectors for points in general position. In particular, we connect the possible configurations 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 positive and negative support vectors in a generic SVM configuration are projected to the separating hyperplane, then these projected points will form a Radon configuration.
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Subject
support vector machines
Radon's theorem