Abstract
Silhouette coefficient is an established internal clustering evaluation measure that produces a score per data point, assessing the quality of its clustering assignment. To assess the quality of the clustering of the whole dataset, the scores of all the points in the dataset are typically (micro) averaged into a single value. An alternative path, however, that is rarely employed, is to average first at the cluster level and then (macro) average across clusters. As we illustrate in this work with a synthetic example, the typical micro-averaging strategy is sensitive to cluster imbalance while the overlooked macro-averaging strategy is far more robust. By investigating macro-Silhouette further, we find that uniform sub-sampling, the only available strategy in existing libraries, harms the measure’s robustness against imbalance. We address this issue by proposing a per-cluster sampling method. An empirical analysis on eight real-world datasets in two clustering tasks reveals the disagreement between the two coefficients for imbalanced datasets.
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Acknowledgements
– This work has been supported by project MIS 5154714 of the National Recovery and Resilience Plan Greece 2.0 funded by the European Union under the NextGenerationEU Program.
– This research project is implemented in the framework of H.F.R.I. call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union - NextGenerationEU (H.F.R.I. ProjectNumber: 15940).
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Pavlopoulos, J., Vardakas, G., Likas, A. (2025). Revisiting Silhouette Aggregation. In: Pedreschi, D., Monreale, A., Guidotti, R., Pellungrini, R., Naretto, F. (eds) Discovery Science. DS 2024. Lecture Notes in Computer Science(), vol 15243. Springer, Cham. https://doi.org/10.1007/978-3-031-78977-9_23
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