Explainable cluster analysis: a bagging approach

A major limitation of clustering approaches is their lack of explainability: methods rarely provide insight into which features drive the grouping of similar observations. To address this limitation, we propose an ensemble-based clustering framework that integrates bagging and feature dropout to generate feature importance scores, in analogy with feature importance mechanisms in supervised random forests. By leveraging multiple bootstrap resampling schemes and aggregating the resulting partitions, the method improves stability and robustness of the cluster definition, particularly in small-sample or noisy settings. Feature importance is assessed through an information-theoretic approach: at each step, the mutual information between each feature and the estimated cluster labels is computed and weighted by a measure of clustering validity to emphasize well-formed partitions, before being aggregated into a final score. The method outputs both a consensus partition and a corresponding measure of feature importance, enabling a unified interpretation of clustering structure and variable relevance. Its effectiveness is demonstrated on multiple simulated and real-world datasets.

A Bayesian Approach to Clustering via the Proper Bayesian Bootstrap: the Bayesian Bagged Clustering (BBC) algorithm

The paper presents a novel approach for unsupervised techniques in the field of clustering. A new method is proposed to enhance existing literature models using the proper Bayesian bootstrap to improve results in terms of robustness and interpretability. Our approach is organized in two steps: k-means clustering is used for prior elicitation, then proper Bayesian bootstrap is applied as resampling method in an ensemble clustering approach. Results are analyzed introducing measures of uncertainty based on Shannon entropy. The proposal provides clear indication on the optimal number of clusters, as well as a better representation of the clustered data. Empirical results are provided on simulated data showing the methodological and empirical advances obtained.