The proximity of an individual to a population withapplications in discriminant analysisC

We develop a proximity function between an individual and a population from a distance between multivariate observations. We study some properties of this construction and apply it to a distance{based discrimination rule, which contains the classic linear discriminant function as a particular case. Additionally, this rule can be used advantageously for categorical or mixed variables, or in problems where a probabilistic model is not well determined. This approach is illustrated and compared with other classic procedures using four real data sets. The authors thank M.Abrahamowicz, J.C. Gower and M. Greenacre for their helpful comments, and W.J. Krzanowski for providing us with a data set and his quadratic location model program.