A Generalized Kernel Approach to Dissimilarity-based Classification

Abstract

Usually, objects to be classified are represented by features. In this paper, we discuss an
alternative object representation based on dissimilarity values. If such distances separate
the classes well, the nearest neighbor method offers a good solution. However, dissimilarities
used in practice are usually far from ideal and the performance of the nearest neighbor rule
suffers from its sensitivity to noisy examples. We show that other, more global classification
techniques are preferable to the nearest neighbor rule, in such cases.
For classification purposes, two different ways of using generalized dissimilarity kernels
are considered. In the first one, distances are isometrically embedded in a pseudo-Euclidean
space and the classification task is performed there. In the second approach, classifiers are
built directly on distance kernels. Both approaches are described theoretically and then
compared using experiments with different dissimilarity measures and datasets including
degraded data simulating the problem of missing values.
Keywords: dissimilarity, embedding, pseudo-Euclidean space, nearest mean classifier,
support vector classifier, Fisher linear discriminant