Modi...ed biplots for enhancing two-class discriminant analysis

When applied to discriminant analysis (DA) biplot methodology leads to useful graphical displays for describing and quantifying multidimensional separation and overlap among classes. The principles of ordinary scatterplots are extended in these plots by adding information of all variables on the plot. However, we show that there are fundamental di¤erences between two-class DA problems and the case J > 2: describing overlap in the two-class situation is relatively straightforward using density estimates but adding information by way of multiple axes to the plot can be ambiguous unless care is taken. Contrary to this, describing overlap for J > 2 classes is relatively more complicated but the ...tting of multiple calibrated axes to biplots is well de...ned. We propose modi...cations to existing biplot methodology leading to useful biplots for use in the important case of two-class DA problems.