Biplots of compositional data

J. Aitchison and Michael Greenacre

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

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 (search for similar items in EconPapers)
JEL-codes: C19 C88 (search for similar items in EconPapers)
Date: 2001-06
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Biplots of compositional data (2002)
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Persistent link: https://EconPapers.repec.org/RePEc:upf:upfgen:557

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