Counterfactual Explanations for k-means and Gaussian Clustering

TL;DR

This paper introduces a novel method for generating counterfactual explanations for clustering algorithms like k-means and Gaussian clustering, incorporating constraints for plausibility and feasibility to enhance interpretability.

Contribution

It provides the first formal framework for counterfactual explanations in clustering, with analytical solutions for k-means and numerical methods for Gaussian models.

Findings

Analytical formulas for k-means counterfactuals

Numerical solutions for Gaussian clustering counterfactuals

Demonstrated advantages through experiments

Abstract

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.