An R package for silhouette-based diagnostics in standard, soft, and multi-way clustering.
Quantifies clustering quality by measuring both cohesion within clusters and separation between clusters. Implements advanced silhouette width computations for diverse clustering structures, including: simplified silhouette by Van der Laan et al. (2003), Probability of Alternative Cluster normalization methods by Raymaekers & Rousseeuw (2022), fuzzy clustering and silhouette diagnostics using membership probabilities by Campello & Hruschka (2006) and Bhat & Kiruthika (2024), and multi-way clustering extensions such as block and tensor clustering by Schepers et al. (2008) and Bhat & Kiruthika (2025). Provides tools for computation and visualisation based on Rousseeuw (1987) to support robust and reproducible cluster diagnostics across standard, soft, and multi-way clustering settings.
Installation
You can install the released version of Silhouette from GitHub using:
# Install devtools if needed
if (!requireNamespace("devtools", quietly = TRUE)) {
install.packages("devtools")
}
# Install from GitHub
devtools::install_github("kskbhat/Silhouette")From CRAN, install via:
install.packages("Silhouette")Usage
Usage of the main functions is demonstrated in the package examples and documentation.
For an intro, see the vignette A quick tour of Silhouette, which is available as
vignette("Silhouette")You can access the vignette from the User Guide tab in the top navigation bar of the package’s website.
References
Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65. doi:10.1016/0377-0427(87)90125-7
Van der Laan, M., Pollard, K., & Bryan, J. (2003). A new partitioning around medoids algorithm. Journal of Statistical Computation and Simulation, 73(8), 575–584. doi:10.1080/0094965031000136012
Campello, R. J., & Hruschka, E. R. (2006). A fuzzy extension of the silhouette width criterion for cluster analysis. Fuzzy Sets and Systems, 157(21), 2858–2875. doi:10.1016/j.fss.2006.07.006
Schepers, J., Ceulemans, E., & Van Mechelen, I. (2008). Selecting among multi-mode partitioning models of different complexities: A comparison of four model selection criteria. Journal of Classification, 25(1), 67–85. doi:10.1007/s00357-008-9005-9
Kassambara, A., & Mundt, F. (2020). factoextra: Extract and Visualize the Results of Multivariate Data Analyses. R package version 1.0.7. doi:10.32614/CRAN.package.factoextra
Raymaekers, J., & Rousseeuw, P. J. (2022). Silhouettes and quasi residual plots for neural nets and tree-based classifiers. Journal of Computational and Graphical Statistics, 31(4), 1332–1343. doi:10.1080/10618600.2022.2050249
Bhat Kapu, S., & Kiruthika. (2024). Some density-based silhouette diagnostics for soft clustering algorithms. Communications in Statistics: Case Studies, Data Analysis and Applications, 10(3–4), 221–238. doi:10.1080/23737484.2024.2408534
Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., & Hornik, K. (2025). cluster: Cluster Analysis Basics and Extensions. R package version 2.1.8.1. doi:10.32614/CRAN.package.cluster
Bhat Kapu, S., & Kiruthika, C. (2025). Block Probabilistic Distance Clustering: A Unified Framework and Evaluation. PREPRINT (Version 1) available at Research Square. doi:10.21203/rs.3.rs-6973596/v1