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1 SummaryThe 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

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Various applications of correspondence analysis to biomedical data are presented. The basic concepts of profile, mass and chi-squared distance are introduced in an initial simple example using data on the relationship between headache types and age. The main result of the correspondence analysis is a geometric map of this relationship showing how the relative frequencies of headache types change with age. A second example maps the association between personality types and various medical diagnostic groups, while a third example deals with categorical rating scales such as an efficacy scale for a medication or a scale of pain. A final example illustrates the more complex situation when several categorical variables are involved using test data on a collection of bacterial isolates, with the object of comparing bacterial types and understanding the inter-relationships of the different tests.