# Silhouette score: counter-intuitive results

so I was looking back at this tutorial (https://scikit-learn.org/stable/auto_examples/cluster/plot_kmeans_silhouette_analysis.html) and it struck me that the example with clusters=4, the one I would have chosen "visually" was not the one with the highest score. Instead n_clusters=2 was chosen, something I would not have chosen

below the scores (taken verbatim from the tutorial)

For n_clusters = 2 The average silhouette_score is : 0.7049787496083262
For n_clusters = 3 The average silhouette_score is : 0.5882004012129721
For n_clusters = 4 The average silhouette_score is : 0.6505186632729437
For n_clusters = 5 The average silhouette_score is : 0.56376469026194
For n_clusters = 6 The average silhouette_score is : 0.4504666294372765


what am I missing? what would I need to change to have the option with clusters=4 be the winning one?

• 1) Criterion vs eye. If data are interval, clusters are not infrequently discernible visually.... 2) There exist 100+ different internal clustering criteria. Silhouette is only one of them. Why not try other? Why not try, say, another version of Silhouette criterion, called "Deviation Silhouette aka Simplified Silhouette"? Oct 16 '21 at 10:20
• Yes at the end I have been trying a combination of different scores and it's working much better! Oct 18 '21 at 11:43