Projections Distinguishing Isolated Groups in Multivariate Data Spaces

Abstract

When multivariate data are available from various different groups of objects, one may wish to discern the most “extreme” groups in the multivariate data space. Four procedures are proposed for finding projections of the high-dimensional data configuration onto a small number of dimensions along which such groups are distinguished best. These procedures involve maximization of either a sum of correlation ratios, or a sum of between-groups variances. It is shown that the use of correlation ratios often leads to trivial dimensions corresponding to directions in the configuration along which the data hardly vary.