Counterfactuals for Feature-Weighted Clustering

2026-07-16

AI Summary

This study addresses the challenge of generating effective and interpretable counterfactual explanations for unsupervised feature-weighted clustering—specifically, identifying the minimal input perturbations required to shift a sample into a target cluster. To this end, the authors propose the VoICE framework, which uniquely incorporates full weighted Voronoi regions into counterfactual generation. By projecting samples onto the weighted Voronoi cell of the target cluster, VoICE jointly accounts for feature weights, feasibility constraints, and data boundary limitations, while employing homogeneity-aware shrinkage to mitigate extrapolation risks and enhance boundary sensitivity. Experimental results demonstrate that VoICE consistently produces valid counterfactuals across multiple benchmark datasets, significantly outperforming existing methods that rely solely on pairwise cluster boundaries.

Abstract

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.

Problem

• counterfactual explanations
• feature-weighted clustering
• k-means clustering
• Voronoi regions
• unsupervised learning

Innovation

• counterfactual explanations
• feature-weighted k-means
• Voronoi regions
• interpretable clustering
• actionability constraints