Principal Components Analysis (PCA) starts directly from a character table to obtain non-hierarchic groupings in a multi-dimensional space. Any combination of components can be displayed in two or three dimensions. Discriminant analysis is very similar to PCA. The major difference is that PCA calculates the best discriminating components without foreknowledge about groups, whereas discriminant analysis calculates the best discriminating components (= discriminants) for groups that are defined by the user.
The advanced presentation modes of PCA and discriminant analysis produce fascinating three-dimensional graphs in a user-definable X-Y-Z coordinate system, which can rotate in real time to enhance the perception of the spatial structures. Entry groups can be delineated using colors and/or codes. For advanced grouping comparisons and methodological validations, dendrogram branches can be plotted on the 3-D representation.