Silhouette
For each case, silhouette compares average within-cluster dissimilarity with the best neighboring-cluster dissimilarity. Values range from −1 to 1: near 1 indicates substantially better fit to its assigned cluster, near 0 a boundary case, and negative values possible misassignment.1
Rousseeuw proposed descriptive bands such as .71–1 strong structure, .51–.70 reasonable, .26–.50 weak, and ≤.25 no substantial structure.1
| Value | Original reading | Category |
|---|---|---|
| .71–1.00 | Strong structure | ORIGINAL CONVENTION |
| .51–.70 | Reasonable structure | ORIGINAL CONVENTION |
| .26–.50 | Weak or artificial structure | ORIGINAL CONVENTION |
| ≤.25 | No substantial structure | ORIGINAL CONVENTION |
These depend on the distance, scaling, algorithm, and candidate cluster count.
Brier score and calibration
For binary outcomes, Brier score averages (predicted probability − outcome)², with lower values better.2 Its scale depends on prevalence and case mix. Compare against a reference forecast and decompose or supplement it with calibration and discrimination evidence.
A calibration plot groups or smooths predictions and compares them with observed frequencies. Perfect calibration lies on the diagonal, but small samples can make the plot noisy. Calibration does not guarantee discrimination, and AUC interpretation does not guarantee calibration.
F1 score uses thresholded classifications rather than probability accuracy. Provenance guidance explains why one task’s numeric target cannot become a universal threshold.
A compact interpretation walkthrough
Suppose a clustering run has mean silhouette .56, while a probability model has Brier score .12 and a reference forecast has Brier score .18. The silhouette value can be described as reasonable structure under Rousseeuw’s convention, subject to the chosen distance and scaling. The lower Brier score improves on that stated reference, but it still needs a calibration plot to show where predicted probabilities are systematically too high or too low.
Do not compare .56 with .12 and conclude that the larger number is better. The metrics have different directions, ranges, reference points, and user jobs.
A defensible reporting sentence
“Mean silhouette was .56 under the stated distance and scaling, a reasonable structure under Rousseeuw’s convention. The probability model’s Brier score beat the baseline, while its calibration plot showed overprediction in the highest-risk range.”