On Searching for the Most Informative Spatial Pattern

This paper is concerned with an inquiry into the way in which the organisation of a spatial data set affects the interpretation of the spatial phenomena which it records, in terms of its underlying pattern or density. It is argued that the number and configuration of zones affects the level of information which is imparted to the spatial analyst, and thus the quest becomes one in which the data set is to be reorganised spatially to impart maximum information. The paper sets out to define an appropriate measure of information and an algorithm designed to optimise its value. The information measure developed is in essence a modified Shannon entropy, modified to account for uneven zonal configurations and converging to Shannon entropy when the zoning system is equal-area and the distribution the best approximation to the density. The measure has some well-known aggregation properties which are presented and several interpretations of its form in spatial terms are made. Empirical measurements of this information measure on the distribution of population in seven metropolitan areas indicate that by aggregation of zones to equal areas, increases in information might be possible and a clearer picture of the underlying density perceived. Accordingly a simple algorithm embodying an heuristic to optimise towards the equal-area norm is developed and applied to the Los Angeles region. The results, in fact, indicate that information cannot be improved in this case, and this leads to a reexamination of the nature of the problem and to suggestions for further research.