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

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 ( 𝔘 Par- ν -SVM). Unlabeled samples can be integrated into supervised learning by means of 𝔘 Par- ν -SVM. We propose a fast method to solve the suggested problem of 𝔘 Par- ν -SVM. The primal problem of 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- 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.