An Algorithm for Reducing the Number of Support Vectors

Abstract

According to the Support Vector Machine algorithm, the task of classification depends on a subset of the original data-set, which is the set of Support Vectors (SVs). They are the only information needed to compute the discriminating function between the classes and, therefore, to classify new data. Since both the computational complexity and the memory requirements of the algorithm depend on the number of SVs, this property is very appealing from the point of view of hardware implementations. For this reason, many researchers have proposed new methods to reduce the number of SVs, even at the expenses of a larger error rate. We propose in this work a method which aims at finding a single point per each class, called archetype, which allows to reconstruct the classifier found by the SVM algorithm, without suffering any classification rate loss. The method is also extended to the case of non-linear classification by finding an approximation of the archetypes in the input space, which maintain the ability to classify the data with a moderate increase of the error rate.