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Silhouette-upper-bound: An upper bound on the silhouette evaluation metric for clustering

Hugo Sträng & Tai Dinh

Software Impacts2026https://doi.org/10.1016/j.simpa.2026.100835article
AJG 1
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0.50

What the paper says

Silhouette-upper-bound is an open-source Python package that computes data-dependent upper bounds for the Average Silhouette Width (ASW), providing a dataset-specific ceiling for silhouette-based clustering evaluation. Unlike the generic theoretical maximum of 1, the proposed bound reflects intrinsic geometric limitations imposed by a chosen dissimilarity matrix, enabling more meaningful interpretation of achieved silhouette scores. The package offers (i) sharp pointwise upper bounds for each observation, (ii) a dataset-level ASW upper bound obtained by aggregation, (iii) restricted bounds under a minimum cluster-size constraint via parameter m , and (iv) an upper bound for the macro-averaged silhouette under fixed cluster sizes. • Introduces a data-dependent upper bound on Average Silhouette Width (ASW). • Sharp pointwise bounds enable sample-level silhouette diagnostics. • Supports minimum cluster size via m for realistic ceilings. • Upper-bounds macro-averaged silhouette under fixed cluster sizes. • Helps compare clustering results by measuring closeness to the upper bound.

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https://doi.org/https://doi.org/10.1016/j.simpa.2026.100835

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@article{hugo2026,
  title        = {{Silhouette-upper-bound: An upper bound on the silhouette evaluation metric for clustering}},
  author       = {Hugo Sträng & Tai Dinh},
  journal      = {Software Impacts},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1016/j.simpa.2026.100835},
}

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Evidence weight

0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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