# Clustering by Direct Optimization of the Medoid Silhouette

arXiv: https://arxiv.org/abs/2209.12553 · HTML: https://mlsanity.com/paper/2209.12553/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 20 references that are in the map.
- First posted on arXiv 26 Sep 2022.

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

- [Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/1810.05691/) (2018)
- [Fast and Eager k-Medoids Clustering: O(k) Runtime Improvement of the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/2008.05171/) (2020)

## Built on by (most cited first, 4 of 4)

- [Stop using the elbow criterion for k-means and how to choose the number of clusters instead](https://mlsanity.com/paper/2212.12189/) (2022)
- [CARL-G: Clustering-Accelerated Representation Learning on Graphs](https://mlsanity.com/paper/2306.06936/) (2023)
- [An upper bound on the silhouette evaluation metric for clustering](https://mlsanity.com/paper/2509.08625/) (2025)
- [Robust K-means Clustering using the Density Power Divergence Measure](https://mlsanity.com/paper/2608.30093/) (2026)

## Abstract (arXiv)

The evaluation of clustering results is difficult, highly dependent on the evaluated data set and the perspective of the beholder. There are many different clustering quality measures, which try to provide a general measure to validate clustering results. A very popular measure is the Silhouette. We discuss the efficient medoid-based variant of the Silhouette, perform a theoretical analysis of its properties, and provide two fast versions for the direct optimization. We combine ideas from the original Silhouette with the well-known PAM algorithm and its latest improvements FasterPAM. One of the versions guarantees equal results to the original variant and provides a run speedup of O(k2). In experiments on real data with 30000 samples and k=100, we observed a 10464× speedup compared to the original PAMMEDSIL algorithm.