In a nutshell, regionalized classification is the probabilistic assigment of sites to groups employing discriminant analysis. Discriminant analysis requires a training set that in regionalized classification ordinarily is prepared using cluster analysis. Preparation of maps may require the interpolation of group probabilities that may be done by kriging. In classical applications of discriminant analysis, one employs a training set including direct indicators of group membership.
Medical science provides good examples.
In certain instances, a group of sick patients is carefully examined to prepare a clinical record relating internal conditions to their external symptoms and laboratory analyses, a costly and lengthy classification only possible after performing surgery or autopsy. In this context, based only on external symptoms and laboratory analyses, the task of discriminant analysis is to determine the probability that other patients suffer the internal conditions considered in the training set. In earth sciences what prevails is the equivalent of knowing only the external symptoms and never knowing the group assignments. Even worse, the nature and number of the groups is seldom known. Determining the groups is as important in such studies as the assignments themselves.