# Robust Trimmed k-means

arXiv: https://arxiv.org/abs/2108.07186 · HTML: https://mlsanity.com/paper/2108.07186/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 38 references that are in the map.
- First posted on arXiv 16 Aug 2021.

## Builds on (most cited first, 3 of 3)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [A unified sparse optimization framework to learn parsimonious physics-informed models from data](https://mlsanity.com/paper/1906.10612/) (2019)
- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)

## Built on by (most cited first, 5 of 5)

- [A Scalable Algorithm for Individually Fair K-means Clustering](https://mlsanity.com/paper/2402.06730/) (2024)
- [No More Than 6ft Apart: Robust K-Means via Radius Upper Bounds](https://mlsanity.com/paper/2203.02502/) (2022)
- [Consistency and inconsistency in k-means clustering](https://mlsanity.com/paper/2507.06226/) (2025)
- [Distributionally Robust K-Means Clustering](https://mlsanity.com/paper/2604.11118/) (2026)
- [Lloyd's K-Means Clustering Algorithm Is Frank-Wolfe in Disguise](https://mlsanity.com/paper/2607.25190/) (2026)

## Abstract (arXiv)

Clustering is a fundamental tool in unsupervised learning, used to group objects by distinguishing between similar and dissimilar features of a given data set. One of the most common clustering algorithms is k-means. Unfortunately, when dealing with real-world data many traditional clustering algorithms are compromised by lack of clear separation between groups, noisy observations, and/or outlying data points. Thus, robust statistical algorithms are required for successful data analytics. Current methods that robustify k-means clustering are specialized for either single or multi-membership data, but do not perform competitively in both cases. We propose an extension of the k-means algorithm, which we call Robust Trimmed k-means (RTKM) that simultaneously identifies outliers and clusters points and can be applied to either single- or multi-membership data. We test RTKM on various real-world datasets and show that RTKM performs competitively with other methods on single membership data with outliers and multi-membership data without outliers. We also show that RTKM leverages its relative advantages to outperform other methods on multi-membership data containing outliers.