Counterfactual Explanations for k-means and Gaussian Clustering
This work addresses the need for interpretability in clustering for users in data science and AI, representing an incremental extension of counterfactual methods from classification to clustering.
The paper tackles the problem of explaining clustering solutions by introducing counterfactual explanations for k-means and Gaussian clustering, providing analytical formulas for k-means and numerical methods for Gaussian cases with experimental validation.
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.