Regularized K-means through hard-thresholding

TL;DR

This paper introduces HT K-means, a regularized clustering method using an $ ext{l}_0$ penalty to promote sparsity, with theoretical analysis, simulation comparisons, and real data applications.

Contribution

It proposes a novel HT K-means algorithm with an $ ext{l}_0$ penalty, and compares various penalization strategies through simulations and real data analysis.

Findings

HT K-means performs favorably compared to existing methods.

Different tuning parameter selection techniques are evaluated.

The method provides insightful visualizations for datasets.

Abstract

We study a framework of regularized $K$-means methods based on direct penalization of the size of the cluster centers. Different penalization strategies are considered and compared through simulation and theoretical analysis. Based on the results, we propose HT $K$-means, which uses an $\ell_0$ penalty to induce sparsity in the variables. Different techniques for selecting the tuning parameter are discussed and compared. The proposed method stacks up favorably with the most popular regularized $K$-means methods in an extensive simulation study. Finally, HT $K$-means is applied to several real data examples. Graphical displays are presented and used in these examples to gain more insight into the datasets.