Abstract

Abstract — Kernel methods are well established and successful algorithms for pattern analysis thanks to their mathematical elegance and efficient solutions they provide. Numerous nonlinear extensions of pattern recognition techniques have been proposed based on the so-called kernel trick. The objective of this paper is twofold. First, we derive an additional kernel tool, namely kernel quadratic discriminant (KQD). We discuss different formulations of KQD based on the regularized kernel Mahalanobis distance in both full and classrelated subspaces. Secondly, we propose suitable extensions of kernel linear and quadratic discriminants to indefinite kernels. We provide classifiers that are applicable to kernels defined by any symmetric similarity measure. This is important in practice because problem-suited proximity measures often disobey the requirement of positive definiteness. As in the traditional case, KQD can be advantageous for data with unequal class spreads in the kernel-induced spaces, which cannot be well separated by a linear discriminant. We illustrate this on artificial and real data for both positive definite and indefinite kernels.