On the Existence of Kernel Function for Kernel-Trick of k -Means in the Light of Gower Theorem

Abstract

This paper, constituting an extension to the conference paper [1], corrects the proof of the Theorem 2 from the Gower’s paper [2, page 5]. The correction is needed in order to establish the existence of the kernel function used commonly in the kernel trick e.g. for k-means clustering algorithm, on the grounds of distance matrix. The correction encompasses the missing if-part proof and dropping unnecessary conditions.