On the Discrepancy Between Kleinberg's Clustering Axioms and k-Means Clustering Algorithm Behavior

02/15/2017
by   Robert Kłopotek, et al.
0

This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called k-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate here on the case predominantly relevant for k-means algorithm, that is behavior embedded in Euclidean space. We point at some contradictions and counter intuitiveness aspects of this axiomatic set within R^m that were evidently not discussed so far. Our results suggest that apparently without defining clearly what kind of clusters we expect we will not be able to construct a valid axiomatic system. In particular we look at the shape and the gaps between the clusters. Finally we demonstrate that there exist several ways to reconcile the formulation of the axioms with their intended meaning and that under this reformulation the axioms stop to be contradictory and the real-world k-means algorithm conforms to this axiomatic system.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/25/2020

Unsupervised K-Means Clustering Algorithm

The k-means algorithm is generally the most known and used clustering me...
research
06/04/2021

Entropy K-Means Clustering With Feature Reduction Under Unknown Number of Clusters

The k-means algorithm with its extensions is the most used clustering me...
research
08/07/2023

Wide Gaps and Clustering Axioms

The widely applied k-means algorithm produces clusterings that violate o...
research
08/30/2022

k-MS: A novel clustering algorithm based on morphological reconstruction

This work proposes a clusterization algorithm called k-Morphological Set...
research
12/11/2014

A Novel Adaptive Possibilistic Clustering Algorithm

In this paper a novel possibilistic c-means clustering algorithm, called...
research
08/18/2023

Do you know what q-means?

Clustering is one of the most important tools for analysis of large data...
research
08/02/2021

Metodos de Agrupamentos em dois Estagios

This work investigates the use of two-stage clustering methods. Four tec...

Please sign up or login with your details

Forgot password? Click here to reset