Translation Invariance in the Polynomial Kernel Space and Its Applications in kNN Classification

Abstract

In this paper, a new technique is presented to measure dissimilarity in kernel space providing scaling and translation invariance. The motivation comes from signal/image processing, where classifiers are often required to ensure invariance against linear transforms, since in many cases linear transforms do not affect the content of a signal/image for a human observer. We examine the theoretical background of linear invariance in the polynomial kernel space, introduce the centered correlation and centered Euclidean dissimilarity in kernel space, deduce formulas to compute it efficiently and test the proposed dissimilarity measures with the kNN classifier. The experimental results show that the presented techniques are highly competitive in similarity or dissimilarity based classification methods.