Aitchison, JohnGreenacre, MichaelUniversitat Pompeu Fabra. Departament d'Economia i Empresa2017-07-262017-07-262001-06-01Applied Statistics, 51, (2002), pp. 375-392http://hdl.handle.net/10230/1046The singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the speciffic case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is demonstrated on a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.application/pdfengL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commonsinfo:eu-repo/semantics/workingPaperlogratio transformationprincipal component analysisrelative variation biplotsingular value decompositionsubcompositionStatistics, Econometrics and Quantitative Methodsinfo:eu-repo/semantics/openAccess