Miara stabilności w wyborze liczby grup w taksonomii zagregowanej z zastosowaniem analizy spektralnej i metody propagacji podobieństwa

Abstract

Since the 1990s, the aggregate approach and the stability of grouping methods have been concepts frequently discussed in the field of taxonomy. So far, they have been considered separately, but recently, there has been a postulate in the literature to combine these two concepts in the form of the PAC (proportion of ambiguously clustered pairs) stability measure, which can be used in the aggregate approach to taxonomy and which is intended to serve as a criterion for selecting an optimal number of groups. The aim of the research presented in this article is to compare the results of the selection of the optimal number of groups in aggregate taxonomy on the example of the attainment of three Sustainable Development Goals (SDGs) by EU countries. The PAC measure and selected classic indices, namely the Caliński-Harabasz, the Dunn and the Davies-Bouldin indices were applied for this purpose. The affinity propagation method and spectral clustering served as base methods in the aggregate approach. The study used Eurostat data for 2019. The obtained results demonstrate that both the choice of the criterion for determining the number of groups and the choice of the base method in aggregate taxonomy have an influence on the final decision on how to determine the number of groups. Regardless of whether the affinity propagation method or spectral taxonomy with classic indices was used, or whether these methods were used as base ones in the aggregate approach and the number of groups was selected using the PAC measure, the differences between the indicated numbers of groups were very large.