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This paper presents VoICE, a novel framework for generating counterfactual explanations in feature-weighted $k$-means clustering by leveraging Voronoi geometry. By integrating feature weights into the clustering process and formulating counterfactual generation as a projection onto the entire weighted Voronoi region, VoICE provides actionable insights that adhere to least-cost and parsimonious principles. The method outperforms traditional pairwise centroid approaches, consistently yielding valid target-cluster memberships across multiple benchmark datasets.
VoICE reveals that counterfactual explanations in clustering can be both actionable and geometrically grounded, outperforming traditional methods in validity and insight.
Counterfactual explanations provide local, interpretable insight by identifying changes to an input that would alter its assigned outcome. Although well established in supervised learning, their extension to clustering is less direct, since cluster assignments are unlabeled and governed by the geometry of the partition. This paper introduces VoICE, a Voronoi-Induced Counterfactual Explainability framework for feature-weighted $k$-means clustering. Rather than treating cluster change as a crossing of a single pairwise centroid boundary, VoICE formulates counterfactual generation as projection onto the full weighted Voronoi region of a target cluster, incorporating feature weights directly into both the clustering geometry and the counterfactual objective to yield least-cost and parsimonious explanations under actionability constraints. Target regions are further intersected with data-derived bounds and homothetically contracted towards their centroids, limiting extrapolation and boundary sensitivity. VoICE consistently produces valid target-cluster membership, across several benchmark datasets, where the leading pairwise baseline does not.