GSLIB-style programs for discriminant analysis and regionalized classification

Abstract

Discriminant analysis is a statistical technique used to predict the group membership of a set of multivariate observations, each of which is assumed to arise from one of a set of distinct classes or groups. Each group is characterized by a certain distribution in multivariate space, and group allocations are based on the similarity of each sample to each group. Assuming multivariate normality, generalized distance measures based on the squared Mahalanobis distance from each sample to each group centroid arise as the natural measure of similarity. One can allocate samples to groups either on the basis of minimum generalized distance or, equivalently, maximum posterior probability of group membership. In earth science applications samples are often associated with geographic locations. In this situation regionalized classification can be used to produce a map representing group membership throughout the sampled domain. This can be accomplished by interpolating either generalized distances or membership probabilities from sample locations to regularly spaced grid nodes and comparing resulting grids to produce a classification map. This paper presents a set of GSLIB-style FORTRAN programs for performing discriminant analysis and regionalized classification. The program disco performs discriminant analysis and the programs xmd2cls and prb2cls combine interpolated distances and probabilities, respectively, to create a grid of predicted classifications. In addition, the utility program colbind allows the user to combine selected columns from different GSLIB-style data files into one file. © 1997 Elsevier Science Ltd.