On lp-support vector machines and multidimensional kernels

Abstract

In this paper, we extend the methodology developed for Support Vector Machines (SVM) using the l2-norm (l2-SVM) to the more general case of lp-norms with p > 1 (lp-SVM). We derive second order cone formulations for the resulting dual and primal problems. The concept of kernel function, widely applied in l2-SVM, is extended to the more general case of lp-norms with p > 1 by de ning a new operator called multidimensional kernel. This object gives rise to reformulations of dual problems, in a transformed space of the original data, where the dependence on the original data always appear as homogeneous polynomials. We adapt known solution algorithms to e ciently solve the primal and dual resulting problems and some computational experiments on real-world datasets are presented showing rather good behavior in terms of the accuracy of lp-SVM with p > 1.