A scale-space clustering method: Mitigating the effect of scale in the analysis of zone-based data

Scale-space clustering methods have a variety of applications in image processing, spatial imagery data mining, classification of land uses, identification of seismic belts, pattern recognition, and more. The full potential of these methods, particularly in a socioeconomic context, has not been realized due to its cumbersome mathematical formulations and lack of implementation in a ready-to-use module for wide distribution. The objectives of this article are threefold: to develop a modified scale-space clustering method (MSSC) that accounts for both attribute homogeneity and spatial contiguity, to implement the method in a geographic information system (GIS) program for wide distribution, and to demonstrate its values in a case study. This is coherent with the intent of developing frame- independent and scale-invariant methods, and has important implications in several spatial analysis issues. For instance, it can be used (1) to construct geographic areas with sufficiently large base population to mitigate the small population problem, (2) to mitigate the modifiable areal unit problem (MAUP) in analyzing zone-based data, and (3) to risk less model-building error in using ordinary least squares (OLS) regression as the clustered zones exhibit less spatial autocorrelation. The case study reveals a converging effect of the clustering process, characterized by an exponential function. A metric, level of convergence, is developed to measure the closeness of area objects in terms of both attribute homogeneity and spatial proximity. Key Words: level of convergence, modifiable areal unit problem (MAUP), modified scale-space clustering (MSSC) method, small population problem, spatial autocorrelation.