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Biplots of compositional data (2002)
| Venue: | Applied Statistics |
| Citations: | 44 - 13 self |
BibTeX
@ARTICLE{Aitchison02biplotsof,
author = {John Aitchison and Michael Greenacre},
title = {Biplots of compositional data},
journal = {Applied Statistics},
year = {2002},
pages = {392}
}
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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 speci¯c 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. 2 1
Keyphrases
compositional data singular value decomposition speci case multivariate data abstract painting data set consisting compositional relationship relative variation biplots biplot methodology positive vector colour ratio accurate biplot many form linear biplot powerful tool possible model six-part colour composition special feature unit sum
