Composite Silhouette: A Subsampling-based Aggregation Strategy

• URL: http://arxiv.org/abs/2604.13816v1
• Date: Wed, 15 Apr 2026 12:49:09 GMT
• Title: Composite Silhouette: A Subsampling-based Aggregation Strategy
• Abstract summary: We introduce Composite Silhouette, an internal criterion for cluster-count selection.<n>It aggregates evidence across repeated subsampled clusterings rather than relying on a single partition.<n>Experiments on synthetic and real-world datasets show that Composite Silhouette effectively reconciles the strengths of micro- and macro-averaging.
• Score: 5.70259485914933
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Determining the number of clusters is a central challenge in unsupervised learning, where ground-truth labels are unavailable. The Silhouette coefficient is a widely used internal validation metric for this task, yet its standard micro-averaged form tends to favor larger clusters under size imbalance. Macro-averaging mitigates this bias by weighting clusters equally, but may overemphasize noise from under-represented groups. We introduce Composite Silhouette, an internal criterion for cluster-count selection that aggregates evidence across repeated subsampled clusterings rather than relying on a single partition. For each subsample, micro- and macro-averaged Silhouette scores are combined through an adaptive convex weight determined by their normalized discrepancy and smoothed by a bounded nonlinearity; the final score is then obtained by averaging these subsample-level composites. We establish key properties of the criterion and derive finite-sample concentration guarantees for its subsampling estimate. Experiments on synthetic and real-world datasets show that Composite Silhouette effectively reconciles the strengths of micro- and macro-averaging, yielding more accurate recovery of the ground-truth number of clusters.

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