Composite Silhouette: A Subsampling-based Aggregation Strategy
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| Format: | Preprint |
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2026
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| _version_ | 1866911595524784128 |
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| author | Semoglou, Aggelos Likas, Aristidis Pavlopoulos, John |
| author_facet | Semoglou, Aggelos Likas, Aristidis Pavlopoulos, John |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_13816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Composite Silhouette: A Subsampling-based Aggregation Strategy Semoglou, Aggelos Likas, Aristidis Pavlopoulos, John Machine Learning 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. |
| title | Composite Silhouette: A Subsampling-based Aggregation Strategy |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.13816 |