Various hyperplane classifiers using kernel feature spaces
Kornél Kovács, András Kocsor · 2003
In machine learning the classification approach may be linear or nonlinear, but it seems that by using the so-called kernel idea, linear methods can be readily generalized to the nonlinear ones. The key idea was originally presented in Aizermann’s paper [1] and it was successfully renewed in the context of the ubiquitous Support Vector Machines (SVM) [2]. The roots of SV methods can be traced back to the need for the determination of the optimal parameters of a separating hyperplane, which can be formulated both in input space or in kernel induced feature spaces. While the former is a linear method, the latter results in a nonlinear counterpart. Optimality can vary from method to method and SVM is just one of several possible approaches. In this paper we present a new family of hyperplane classifiers, that make use of various contrast functions for different optimality aspects. However, in contrast to SVM- where a constrained quadratic optimization is used- some of the proposed methods lead to the unconstrained minimization of convex functions