Maximum‐Difference Barriers: An Alternative Numerical Regionalization Method *

Regionalization is the primary classification problem in geography, although other typologies are sometimes demanded by specific research endeavors. Groupings of area units can produce either contiguous or fragmented patterns. Discontiguous regionalizations may have the advantage of placing truly alike areal units in the same category and are obviously necessary when the similarity of distant places is sought. The same number of contiguous regions, on the other hand, will most likely produce a more regular map pattern, thereby facilitating the transferral of the printed map into a more coherent and more lasting mental image.' Furthermore, many problems, particularly those partitioning space for administrative purposes, demand contiguity. Although some within-group homogeneity is often lost by imposing contiguity, this is a difficulty only for situations with relatively low spatial consistency.a This loss of homogeneity may well be offset by the perceptual advantage of simplicity. Previous quantitative approaches to regional clustering have largely achieved contiguity by prohibiting linkages from occurring unless the two places abut. This contiguity restriction has been employed most often with hierarchical grouping procedures in which the clustering of N places proceeds through N 1 levels of classification to the ultimate aggregation of all units into a single group? At