Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

Abstract

Data collected for the investigation of the environmental and ecological characteristics of a river basin are often in the form of a large three-way array; hence, a particular version of the Tucker model could be applied to gather more information contained in such complex geochemical systems. Indeed, when the data are in compositional form, more attention must be given to the analysis of the numerical data. Recently, the Tucker3 model has been proposed to analyze compositional data characterized by a three-way structure. In this work, a particular version of the Tucker model, known as the weighted\ud principal component analysis, was used to analyze water samples collected from the Arno river (Tuscany, central Italy)\ud in order to evaluate the method’s effectiveness. Several graphical displays have been developed to allow an accurate and complete interpretation of results