Opposite maps for hard margin support vector machines

Abstract

This paper introduces a new approach to building hard margin classifiers based on Opposite Maps (OM). OM is a Self-Organizing Map-based method used for obtaining reduced-set classifiers in the sense of soft margin. As originally proposed, Opposite Maps was used for reducing the training data set and obtaining soft margin reduced-set SVM and LSSVM classifiers. In our new proposal we use Opposite Maps in order to obtain a set of patterns in the overlapping area between positive and negative classes and, a posteriori, to remove them from the default training data set. This process can transform a non-linear problem into a linear one in which a hard-margin classifier like Huller SVM can be applied. This approach assure to get resulting classifiers from a training process without needing to set up the cost parameter C that controls the trade off between allowing training errors and margin maximization. Besides that, but differently from soft-margin classifiers, these obtained classifiers leave the patterns at wrong side of the hyperplane out of the set of support vectors and, therefore, reduced-set hard-margin classifiers come out with few support vectors. © 2013 Springer-Verlag.