# Revisiting Silhouette Aggregation

arXiv: https://arxiv.org/abs/2401.05831 · HTML: https://mlsanity.com/paper/2401.05831/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 32 references that are in the map.
- First posted on arXiv 11 Jan 2024.

## Builds on (most cited first, 2 of 2)

- [Stop using the elbow criterion for k-means and how to choose the number of clusters instead](https://mlsanity.com/paper/2212.12189/) (2022)
- [Minimum adjusted Rand index for two clusterings of a given size](https://mlsanity.com/paper/2002.03677/) (2020)

## Built on by (most cited first, 5 of 5)

- [Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters](https://mlsanity.com/paper/2402.00608/) (2024)
- [Silhouette-Driven Instance-Weighted k-means](https://mlsanity.com/paper/2506.12878/) (2025)
- [An upper bound on the silhouette evaluation metric for clustering](https://mlsanity.com/paper/2509.08625/) (2025)
- [CAKE: Confidence in Assignments via K-partition Ensembles](https://mlsanity.com/paper/2602.18435/) (2026)
- [Composite Silhouette: A Subsampling-based Aggregation Strategy](https://mlsanity.com/paper/2604.13816/) (2026)

## Abstract (arXiv)

Silhouette coefficient is an established internal clustering evaluation measure that produces a score per data point, assessing the quality of its clustering assignment. To assess the quality of the clustering of the whole dataset, the scores of all the points in the dataset are typically (micro) averaged into a single value. An alternative path, however, that is rarely employed, is to average first at the cluster level and then (macro) average across clusters. As we illustrate in this work with a synthetic example, the typical micro-averaging strategy is sensitive to cluster imbalance while the overlooked macro-averaging strategy is far more robust. By investigating macro-Silhouette further, we find that uniform sub-sampling, the only available strategy in existing libraries, harms the measure's robustness against imbalance. We address this issue by proposing a per-cluster sampling method. An experimental study on eight real-world datasets is then used to analyse both coefficients in two clustering tasks.