Silhouette-Driven Instance-Weighted $k$-means

TL;DR

This paper introduces K-Sil, a silhouette-driven weighted $k$-means algorithm that improves clustering robustness by emphasizing confidently assigned instances and adapting weights based on silhouette scores, leading to better performance.

Contribution

The paper proposes a novel weighted $k$-means variant that uses silhouette scores for instance weighting and provides theoretical convergence guarantees.

Findings

Consistent improvements in internal validation metrics across 15 datasets.

Enhanced external validation metrics compared to baseline methods.

Robustness to outliers and ambiguous points demonstrated in experiments.

Abstract

Clustering is a fundamental unsupervised learning task with applications across a wide range of domains. Popular algorithms such as $k$-means are efficient and widely used, but can be sensitive to outliers, ambiguous boundary points, and heterogeneous cluster geometry, which may distort centroid estimates and yield suboptimal partitions. We introduce K-Sil, a silhouette-driven $k$-means variant that, at each iteration, weights points using a centroid-margin proxy for the silhouette score, emphasizing confidently assigned instances while down-weighting borderline or noisy regions. Centroid updates take the form of a softmax-weighted mean, and an adaptive temperature automatically calibrates the sharpness of the weight distribution using a cluster-balanced, macro-averaged, silhouette criterion. Under standard separation conditions, we establish a local convergence result for the induced weighted centroid updates. Experiments on 15 real-world datasets spanning tabular, biomedical, text, and image representations show consistent gains in internal validation metrics and typical improvements in external validation metrics over $k$-means and competitive instance-weighted baselines.