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

We are concerned with finding the orthogonal projection to the plane t hat best displays groups. There are three situations in which this que stion can emerge: when the groups are identified a priori; when the cl asses result from a cluster analysis; and when the parameters of the c lasses are estimated from a distribution mixture method. We propose a ''maximin'' projection where the minimum intermean distance is maximiz ed over the different projections to the plane as the one that best di splays all the groups, especially in the presence of groups with marke dly different sizes; in the case of three groups it reduces to the pla ne defined by the canonical variables. We illustrate the method with o ne artificial and one real data set.