# Regularized K-means through hard-thresholding

arXiv: https://arxiv.org/abs/2010.00950 · HTML: https://mlsanity.com/paper/2010.00950/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [CRAB: Codebook Rebalancing for Bias Mitigation in Generative Recommendation](https://mlsanity.com/paper/2604.05113/) (2026)
- [MNAR-k-means: A k-means Clustering for Data Missing Not at Random with Magnitude-Decaying Probability](https://mlsanity.com/paper/2606.31253/) (2026)
- [Statistical Properties of k-means Clustering for Data Missing Completely at Random](https://mlsanity.com/paper/2607.01945/) (2026)

## Abstract (arXiv)

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 ℓ0 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.