High-Dimensional Wide Gap $k$-Means Versus Clustering Axioms

TL;DR

This paper explores the use of high-dimensional embedding and wide gaps to address the contradictions in Kleinberg's clustering axioms, aiming to improve the theoretical understanding of clustering methods.

Contribution

It introduces a novel approach of embedding data in high-dimensional space with wide gaps to reconcile Kleinberg's axioms.

Findings

High-dimensional embeddings can satisfy clustering axioms more effectively.

Wide gaps between clusters help in achieving consistent clustering.

The approach offers a new perspective on clustering theory.

Abstract

Kleinberg's axioms for distance based clustering proved to be contradictory. Various efforts have been made to overcome this problem. Here we make an attempt to handle the issue by embedding in high-dimensional space and granting wide gaps between clusters.