Multi-criteria selection of text clustering alternatives based on Silhouette and Bootstrap stability

Abstract

The paper investigates the problem of selecting text clustering alternatives under conditions where evaluating the result using only a single internal criterion does not provide a complete understanding of the properties of the resulting partition. The Silhouette score characterizes cluster compactness and separation but does not reflect the reproducibility of the obtained solution when the sample composition changes. Therefore, the aim of the study is to develop and experimentally validate a procedure for multi-criteria selection of text clustering alternatives based on the joint consideration of Silhouette and bootstrap stability. Stability is assessed using repeated bootstrap samples and by comparing the resulting partitions with the baseline clustering solution using the Adjusted Rand Index. Pareto analysis is applied to reconcile the two criteria, making it possible to identify a set of compromise alternatives without introducing arbitrary weighting coefficients. The experimental evaluation was conducted on a thematic corpus derived from an open news text dataset of the British Broadcasting Corporation using KMeans and Ward agglomerative clustering. The results show that Silhouette and bootstrap stability produce different rankings of clustering alternatives. For KMeans, the highest Silhouette value was obtained with ten clusters, whereas the maximum bootstrap stability was observed with five clusters. For Ward clustering, the configurations corresponding to the maximum Silhouette, maximum stability, and highest external quality also differed. This indicates that bootstrap stability cannot be considered a universal criterion of clustering correctness, but it provides additional information about the reproducibility of a clustering solution. Applying Pareto dominance based on Silhouette and bootstrap stability reduced the initial set of eighteen alternatives to three non-dominated configurations, corresponding to a reduction of more than eighty-three percent. Reference thematic labels were not used to construct the Pareto set and were not included among the criteria of the multi-criteria selection; they were used only for external evaluation of the obtained configurations. The findings confirm the feasibility of jointly analyzing internal geometric quality and reproducibility when selecting text clustering alternatives.