Area Biplots

Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to estimate data values. The results of these techniques may be visualized by representing the row and column points jointly in a biplot where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner-product that estimates the corresponding data element. In this paper, we propose a new visualization: after a 90 degrees rotation of the row points, the areas spanned by a triangle of a row point, a column point and the origin estimate the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. Areas can only be produced for two dimensions at a time, but higher dimensional solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots but has general applicability.