Computational assessment of k-means clustering on a Structural Equation Model based index

This paper proposes an alternative method for the choice of the number of centroids in a cluster analysis, when the groups’ order is relevant. Differently from commonly used approaches, aimed at finding the minimum number of clusters, the illustrated method aims at finding the maximum one. Given that the clusters are ordered, this allows to define a granular ranking among them. The k-means partitioning algorithm is applied to an index resulting from a Structural Equation Model. The procedure is implemented on a measure of air pollution in urban areas: a clustering of main Italian cities, according to the optimal number of air pollution levels, is the final result. The analysis’ interpretation provides useful information to design policies aimed at reducing air pollution.