Universum parametric-margin ν-support vector machine for classification using the difference of convex functions algorithm

Hossein Moosaei, Fatemeh Bazikar, Saeed Ketabchi, Milan Hladík

Abstract: Universum data that do not belong to any class of a classification problem can be exploited to utilize prior knowledge to improve generalization performance. In this paper, we design a novel parametric ν-support vector machine with universum data (\( \mathfrak {U} \)Par-ν-SVM). Unlabeled samples can be integrated into supervised learning by means of \( \mathfrak {U} \)Par-ν-SVM. We propose a fast method to solve the suggested problem of \( \mathfrak {U} \)Par-ν-SVM. The primal problem of \( \mathfrak {U} \)Par-ν-SVM, which is a nonconvex optimization problem, is transformed into an unconstrained optimization problem so that the objective function can be treated as a difference of two convex functions (DC). To solve this unconstrained problem, a boosted difference of convex functions algorithm (BDCA) based on a generalized Newton method is suggested (named DC-\(\mathfrak {U} \)Par-ν-SVM). We examined our approach on UCI benchmark data sets, NDC data sets, a handwritten digit recognition data set, and a landmine detection data set. The experimental results confirmed the effectiveness and superiority of the proposed method for solving classification problems in comparison with other methods.