Biplots of Compositional Data

UPF Economics and Business Working Paper No. 557

Posted: 13 Sep 2002

See all articles by John Aitchison

John Aitchison

University of Glasgow, Department of Statistics

Michael Greenacre

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

The 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 specific 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.

Keywords: Logratio transformation, principal component analysis, relative variation biplot, singular value decomposition, subcomposition

JEL Classification: C19, C88

Suggested Citation

Aitchison, John and Greenacre, Michael John, Biplots of Compositional Data. UPF Economics and Business Working Paper No. 557, Available at SSRN: https://ssrn.com/abstract=310229

John Aitchison

University of Glasgow, Department of Statistics ( email )

Adam Smith Business School
Glasgow, Scotland G12 8LE
United Kingdom

Michael John Greenacre (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
34 93 542 25 51 (Phone)
34 93 542 17 46 (Fax)

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