Classification with Kernel Mahalanobis Distance Classifiers

Within the framework of kernel methods, linear data methods have almost completely been extended to their nonlinear counterparts. In this paper, we focus on nonlinear kernel techniques based on the Mahalanobis distance. Two approaches are distinguished here. The first one assumes an invertible covariance operator, while the second one uses a regularized covariance. We discuss conceptual and experimental differences between these two techniques and investigate their use in classification scenarios. For this, we involve a recent kernel method, called Kernel Quadratic Discriminant and, in addition, linear and quadratic discriminants in the dissimilarity space built by the kernel Mahalanobis distances. Experiments demonstrate the applicability of the resulting classifiers. The theoretical considerations and experimental evidence suggest that the kernel Mahalanobis distance derived from the regularized covariance operator is favorable.