Counterfactuals for Feature-Weighted Clustering

Generating counterfactual explanations for clustering is inherently more complex than for supervised learning because cluster assignments are defined by geometric partitions rather than explicit labels. Existing methods often rely on simple pairwise boundaries between centroids, which can lead to invalid cluster assignments or unstable explanations. This paper addresses these limitations by introducing VoICE (Voronoi-Induced Counterfactual Explainability), a framework designed to provide robust, actionable, and parsimonious explanations for feature-weighted k-means clustering.

VoICE treats counterfactual generation as a constrained optimization problem. Instead of looking only at the boundary between two clusters, it considers the entire weighted Voronoi region of a target cluster. The framework incorporates feature weights directly into the geometry of these regions and the optimization objective. To ensure the generated counterfactuals are realistic and stable, the authors introduce a robustness-aware mechanism called homothetic contraction. This technique scales the target Voronoi region toward its centroid, effectively creating a compact, bounded subset of the decision space that avoids extrapolation into unsupported regions and reduces sensitivity to boundary fluctuations.

The authors demonstrate that VoICE consistently produces valid target-cluster membership across various benchmark datasets, outperforming leading pairwise baseline methods that often fail to guarantee the intended cluster assignment. By integrating feature weights into the optimization, VoICE allows for the generation of parsimonious explanations—identifying the smallest subset of actionable features required to move an observation into a target cluster. The framework provides a principled way to balance the proximity of the counterfactual to the original input with the requirement that the result remains within a stable, data-supported region of the feature space.