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Dakota Aquifer Program--Geologic Framework

Hodgeman County Study, part 3 of 12


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. In such a situation one replaces the training set assignments by a typification using another method able to decide both the number and characteristics of the groups. The best alternative is cluster analysis, which aside from any prior information not contained in the data, solves the following problem: given a coregionalization sampling of size n comprising p attributes, is there any evidence for clustering the sites into groups scattered around centroids, as against the alternative hypothesis that they are an unstructured coregionalization?

There are several ways to define and find the clusters depending partly on the metric used to determine proximity among the sites in the p dimensional attribute space, the Euclidean distance being the most common and the only one considered here. The geographical distance is completely ignored both in cluster analysis and in discriminant analysis and is only considered at the final mapping stage of regionalized classification.

There have been many studies comparing various methods of cluster analysis using artificial data sets containing known clusters produced by Monte Carlo methods. In most of these studies the Ward's minimum variance method has been the one with the best overall performance on reproducing the known clusters (SAS, 1990, p. 56).

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Kansas Geological Survey, Dakota Aquifer Program
Updated Sept. 16, 1996.
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