Subspace Projection for Multivariate Selection Problems

A new set of derived variables is proposed for exhibiting grouped multivariate data in a small number of dimensions, in such a way as to highlight `extremeness' of one or more groups relative to the rest of the data. Such display can provide a useful exploratory tool in multivariate ranking and selection problems. We explore four possible measures of `extremeness', and suggest which one is best for practical application. We show that the technique can be used to derive either orthogonal or uncorrelated dimensions for any type of input data, and we give an illustrative example of its use.