The p-Centre machine for regression analysis

Abstract

Support vector machines (SVMs) have become one of the most powerful methods in machine learning for solving classification and regression problems. Finding the SVM solution can be regarded as estimating the centre of the largest hypersphere that can be inscribed in the set of consistent hypotheses called the version space. However, this solution can be inaccurate if the version space is asymmetric or elongated. Several approaches have been proposed to utilize other possible centres of the version space that can improve the generalization performance. Morreti in 2003 proposed an algorithm for finding the centre of a general polytope, the so called p-Centre, using weighted projections. By applying this method, Brückner in 2001 introduced a formulation for solving binary classification problems based on an approximation of the p-Centre of the version space, the so called p-Centre machine. In this paper, we extend the work by Brückner and propose a kernel-based algorithm for regression analysis using the p-Centre method. The concept of the p-Centre of a polytope and version space is also explained. Furthermore, the applications of the proposed method are presented. The preliminary results indicate that the p-Centre-based kernel machine for regression has promising performance compared with the SVM for regression.