A penalized criterion for selecting the number of clusters for K-medians

TL;DR

This paper introduces a penalized criterion for selecting the optimal number of clusters in K-medians clustering, especially effective for contaminated data, and validates it through simulations and R package implementation.

Contribution

It proposes a new penalized risk criterion for choosing the number of clusters in K-medians, with theoretical justification and practical comparison.

Findings

The penalty shape is suitable for K-medians clustering.

The method performs well in simulations with contaminated data.

The approach is implemented in the R package Kmedians.

Abstract

Clustering is a usual unsupervised machine learning technique for grouping the data points into groups based upon similar features. We focus here on unsupervised clustering for contaminated data, i.e in the case where K-medians should be preferred to K-means because of its robustness. More precisely, we concentrate on a common question in clustering: how to chose the number of clusters? The answer proposed here is to consider the choice of the optimal number of clusters as the minimization of a risk function via penalization. In this paper, we obtain a suitable penalty shape for our criterion and derive an associated oracle-type inequality. Finally, the performance of this approach with different types of K-medians algorithms is compared on a simulation study with other popular techniques. All studied algorithms are available in the R package Kmedians on CRAN.