PIECEWISE-AFFINE CLASSIFIERS IN SUPPORT VECTOR MACHINES
Miller, Matthew T.
Royset, Johannes O.
Krener, Arthur J.
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The Support Vector Machine (SVM) model has been a topic of study for over twenty years, and novel approaches to the classification problem using SVM continue to be established. In this work, we develop a new, nonlinear version of SVM based on a piecewise-affine classifier. This class of classifiers constitutes a tractable class beyond the affine functions that enables approximation of nonparametric SVM in high dimensions. We solve the resulting Piecewise-Affine SVM (PA-SVM) model using the Difference-of-Convex Algorithm (DCA) and a stochastic gradient descent (SGD) algorithm. The PA-SVM model is nonconvex, and the algorithms generally only provide locally optimal solutions. Still, they provide for a robust, capable classifier. Results show that by using DCA, the PA-SVM model can significantly reduce training misclassifications relative to the common Affine SVM (A-SVM) model by as much as 92%. Additionally, we show that test set errors can be reduced by as much as 67% compared to A-SVM. We find that solutions are more affected by the number of pieces employed rather than by regularization penalties. These results come from applying the PA-SVM model to three real-world data sets whose total features range from 16 to 41 and whose total observations range from 194 to 1,553.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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