# Counterfactual Explanations for k-means and Gaussian Clustering

arXiv: https://arxiv.org/abs/2501.10234 · HTML: https://mlsanity.com/paper/2501.10234/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 13 references that are in the map.
- First posted on arXiv 17 Jan 2025.

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

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Shallow decision trees for explainable k-means clustering](https://mlsanity.com/paper/2112.14718/) (2021)
- [Global k-means++: an effective relaxation of the global k-means clustering algorithm](https://mlsanity.com/paper/2211.12271/) (2022)
- [Counterfactual Explanations for Clustering Models](https://mlsanity.com/paper/2409.12632/) (2024)

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

- [ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material](https://mlsanity.com/paper/2605.30225/) (2026)
- [UniFair: A unified fair clustering approach based on separation and compactness](https://mlsanity.com/paper/2606.04777/) (2026)
- [Counterfactuals for Feature-Weighted Clustering](https://mlsanity.com/paper/2607.14719/) (2026)

## Abstract (arXiv)

Counterfactuals have been recognized as an effective approach to explain classifier decisions. Nevertheless, they have not yet been considered in the context of clustering. In this work, we propose the use of counterfactuals to explain clustering solutions. First, we present a general definition for counterfactuals for model-based clustering that includes plausibility and feasibility constraints. Then we consider the counterfactual generation problem for k-means and Gaussian clustering assuming Euclidean distance. Our approach takes as input the factual, the target cluster, a binary mask indicating actionable or immutable features and a plausibility factor specifying how far from the cluster boundary the counterfactual should be placed. In the k-means clustering case, analytical mathematical formulas are presented for computing the optimal solution, while in the Gaussian clustering case (assuming full, diagonal, or spherical covariances) our method requires the numerical solution of a nonlinear equation with a single parameter only. We demonstrate the advantages of our approach through illustrative examples and quantitative experimental comparisons.