# Composite Silhouette: A Subsampling-based Aggregation Strategy

arXiv: https://arxiv.org/abs/2604.13816 · HTML: https://mlsanity.com/paper/2604.13816/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 25 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 4 of 4)

- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [From A-to-Z Review of Clustering Validation Indices](https://mlsanity.com/paper/2407.20246/) (2024)
- [Revisiting Silhouette Aggregation](https://mlsanity.com/paper/2401.05831/) (2024)
- [An Exploration of Clustering Algorithms for Customer Segmentation in the UK Retail Market](https://mlsanity.com/paper/2402.04103/) (2024)

## Abstract (arXiv)

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.