Kernel-based nonlinear discriminator with closed-form solution

Abstract

This paper proposes a discriminant criterion for pattern classification, in a higher-dimensional feature space nonlinearly related to the input patterns. With this criterion, a pattern class is discriminated from other classes by minimizing the mean energy of the latter's outputs from a nonlinear function. Adoption of the related reproducing kernel leads us to a solution coinciding with the representation of a nonlinear support vector machine (SVM), and it is called a kernel-based nonlinear discriminator (KND) in this paper. However, in addition to the criterion, KND differentiates itself from a nonlinear SVM with a closed form solution, in which any quadratic programming procedure is avoided. Results of a simple experiment on handwritten digit recognition show the usefulness of the proposed method in pattern discrimination.