Patterns in Geographical Data via Maximum

Classiication is a fundamental operation for data analysis and pattern discovery in Geographical Information Systems. It consists of forming clusters from a large set of data values for presentation in choroplethic maps. Strategies based on a measure of diversity of the values within a class provide a quantitative measure of the quality of the classiication but nding the classes requires (n 3) time, where n is the number of data values. We propose the use of classiication via the Maximum Entropy Discretization (MED) of the probability distribution that is being represented by the choroplethic map. MED is rigorously founded on information theory. We show that our approach results in a method for classiication that allows the analyst to treat the data as univariate or as spatially related. Moreover, the algorithms requires only O(n log n) time, and this requirement reduces to O(n) time if data is already sorted.