Biplots

by J. C. Gower

Biplots are the multivariate analog of scatter plots, using multidimensional scaling to approximate the multivariate distribution of a sample in a few dimensions, to produce a graphical display. In addition, they superimpose representations of the variables on this display, so that the relationships between the sample and the variables can be studied. Like scatter plots, biplots are useful for detecting patterns and for displaying the results found by more formal methods of analysis. In recent years the theory of biplots has been considerably extended. The approach adopted here is geometric, permitting a natural integration of well known methods such as components analysis, correspondence analysis and canonical variate analysis as well as some newer and less well known methods such as nonlinear biplots and biadditive models. Much novel material, which has not been published elsewhere, is presented. This monograph is directed at professional and academic statisticians and statistical co