We performed internal cluster validation using six complementary indices: Silhouette, Calinski-Harabasz, C-index, Dunn index, Davis-Bouldin Score from the clusterCrit package (ver) [ref], and a weighted Bayesian Information Criterion (BIC) approach as described in [Reichl 2018 - Chapter 4.2.2 - Internal Indices](https://repositum.tuwien.at/handle/20.500.12708/3488). Due to computational cost, PCA results representing 90% of variance explained were used as input, and only a random sample proportion of [sample_proportion] was used. These internal cluster indices are linear, using Euclidean distance metrics. To rank all clustering results and [metadata_of_interest] from best to worst, we applied the Multiple-criteria decision-making (MCDM) method TOPSIS from the the Python package pymcdm (ver) [ref] to the internal cluster indices, as described in [Reichl 2018 - Chapter 4.3.1 - The Favorite Approach](https://repositum.tuwien.at/handle/20.500.12708/3488).
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