# Adaptively Robust and Sparse K-means Clustering

arXiv: https://arxiv.org/abs/2407.06945 · HTML: https://mlsanity.com/paper/2407.06945/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 32 references that are in the map.
- First posted on arXiv 9 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Robust k-means Clustering for Distributions with Two Moments](https://mlsanity.com/paper/2002.02339/) (2020)
- [Parsimonious mixtures of multivariate contaminated normal distributions](https://mlsanity.com/paper/1305.4669/) (2013)
- [Robust improper maximum likelihood: tuning, computation, and a comparison with other methods for robust Gaussian clustering](https://mlsanity.com/paper/1406.0808/) (2014)
- [Robust and sparse k-means clustering for high-dimensional data](https://mlsanity.com/paper/1709.10012/) (2017)
- [Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties](https://mlsanity.com/paper/1505.05257/) (2015)
- [Robust sparse Gaussian graphical modeling](https://mlsanity.com/paper/1508.05571/) (2015)
- [Robust Fitting of Mixture Models using Weighted Complete Estimating Equations](https://mlsanity.com/paper/2004.03751/) (2020)

## Built on by (most cited first, 1 of 1)

- [Distributionally Robust K-Means Clustering](https://mlsanity.com/paper/2604.11118/) (2026)

## Abstract (arXiv)

While K-means is known to be a standard clustering algorithm, its performance may be compromised due to the presence of outliers and high-dimensional noisy variables. This paper proposes adaptively robust and sparse K-means clustering (ARSK) to address these practical limitations of the standard K-means algorithm. For robustness, we introduce a redundant error component for each observation, and this additional parameter is penalized using a group sparse penalty. To accommodate the impact of high-dimensional noisy variables, the objective function is modified by incorporating weights and implementing a penalty to control the sparsity of the weight vector. The tuning parameters to control the robustness and sparsity are selected by Gap statistics. Through simulation experiments and real data analysis, we demonstrate the proposed method's superiority to existing algorithms in identifying clusters without outliers and informative variables simultaneously.