A stochastic multi-criteria divisive hierarchical clustering algorithm

Clustering is a long and widely-used technique to group similar objects based on their distance. Recently, it has been found that this grouping exercise can be enhanced if the preference information of a decision-maker is taken into account. Consequently, new multi-criteria clustering methods have been proposed. All of our proposed algorithms are based on the non-hierarchical clustering approach, in which the number of clusters is known in advance. In this paper, we propose a new hierarchical multi-criteria clustering that is based on PROMETHEE, where the number of clusters does not need to be specified. Because the outcome is dependent on the parameters of PROMETHEE, we take into account uncertainty and imprecision by enhancing our approach making use of the Stochastic Multiobjective Acceptability Analysis (SMAA) and cluster ensemble methods. SMAA is used to generate a large number of solutions by randomly varying the PROMETHEE parameters, followed by the use of ensemble clustering, which reaches a consensus solution. Our new approach is illustrated in a clustering study of the performance evaluation of US banks according to a set of financial and non-financial (i.e. environmental, social and corporate governance; ESG) criteria. We find that established banks appear in the overall best-performing clusters, with more contemporary banks following suit. In additional analysis we compare financial and overall (financial and non-financial) performance, and find a mixed appreciation of the ESG aspects in this industry in the middle clusters.