The Silhouette coefficient and the Davies-Bouldin index are more informative than Dunn index, Calinski-Harabasz index, Shannon entropy, and Gap statistic for unsupervised clustering internal evaluation of two convex clusters
Why this work is in the frame
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Bibliographic record
Abstract
Clustering is an area of unsupervised machine learning where a computational algorithm groups together similar points into clusters in a meaningful way, according to the algorithm’s properties. When external ground truth for the clustering results assessment is available, researchers can employ an external clustering assessment metrics and evaluate the quality of the clustering results this way. When no external gold standard is available, however, researchers need to use metrics for internal clustering assessment, which produce an outcome just considering the internal data points of the clusters identified. Although consensus regarding the usage of the adjusted Rand index for the external clustering assessment exists, there is no standard regarding internal metrics. We fill this gap by presenting this study on comparing the six internal metrics clustering most commonly used in bioinformatics and health informatics: Silhouette coefficient, Davies-Bouldin index, Dunn index, Calinski-Harabasz index, Shannon entropy, and Gap statistic. We first analyze their mathematical properties, and then test them on the results of k -means with k = 2 clusters on multiple different convex-shaped artificial datasets and on five real-world open medical datasets of electronic health records. Our results show that the Silhouette coefficient and the Davies-Bouldin index are more informative and reliable than the other analyzed rates, when assessing convex-shaped and non-nested clusters in the Euclidean space.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it