# Validity of Clusters Produced By kernel-k-means With Kernel-Trick

arXiv: https://arxiv.org/abs/1701.05335 · HTML: https://mlsanity.com/paper/1701.05335/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Towards Continuous Consistency Axiom](https://mlsanity.com/paper/2202.06015/) (2022)

## Abstract (arXiv)

This paper corrects the proof of the Theorem 2 from the Gower's paper cite[page 5]Gower:1982 as well as corrects the Theorem 7 from Gower's paper citeGower:1986. The first 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. The second correction deals with transformation of the kernel matrix into a one embeddable in Euclidean space.