Geographical Filters and their Inverses*

Abstract

Science proceeds by detecting structures embedded in observational data. It is no simple matter to separate these general structures from the specific details. Many analytical techniques have been designed to do just this; to separate the important from the unimportant. Among the best known of these are statistical methods of accounting for the variability in the observations. The popularity of techniques which yield ordered results (stepwise regression, principal components analysis, or clustering methods, for example) thus becomes clear.Geographical versions of data filtering occur frequently in cartography. Maps are generalized representations since it is clearly impossible to display reality in all its complexity at a reduced scale. Not too surprisingly, map makers are unable to provide explicit abstract statements about the process of map generalization, but some empirical evidence suggests constancy of information content per map centimeter squared, regardless of map scale [5'7]. As Perkal[58] and Tobler [5Z] point out, this is an area for interesting research. Clustering techniques have obvious applicability to dot map generalization [SI] ; network simplification and algorithms do not appear nearly as well developed [Z, 16,40,59]. Even the venerable techniques of regionalization, as forms of data simplification, can probably be improved [&I. Trend AnalysisMost recently popularized have been filtering methods for the analysis of geographical trends [lo]. These are simple extensions of

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