On the Existence of Kernel Function for Kernel-Trick of k-Means

摘要

This paper corrects the proof of the Theorem 2 from the Gower's paper [1, p. 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.