CRITERIA TO REPRESENT GROUPS IN THE PLANE WHEN THE GROUPING IS KNOWN

We are concerned with finding the orthogonal projection to the plane that best displays groups. There are three situations in which this question can emerge: when the groups are identified a priori; when the classes result from a cluster analysis; and when the parameters of the classes are estimated from a distribution mixture method. We propose a ''maximin'' projection where the minimum intermean distance is maximized over the different projections to the plane as the one that best displays all the groups, especially in the presence of groups with markedly different sizes; in the case of three groups it reduces to the plane defined by the canonical variables. We illustrate the method with one artificial and one real data set.