Paper #557

Title:

Biplots of compositional data

Authors:

J. Aitchison and Michael Greenacre

Date:

June 2001

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 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.

Keywords:

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

JEL codes:

C19, C88

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

Applied Statistics, 51, (2002), pp. 375-392

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