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 ...
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.
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