Forming spatially coherent regions by classification of multi-variate data: an example from the analysis of maps of crop yield

A method is proposed for the generation, from multi-variate data, of classes with a spatially coherent distribution. The procedure is more appropriate for large data sets than is spatially constrained clustering based on modification of a similarity matrix. It is based on fuzzy clustering of the data, followed by spatially weighted averaging of the class memberships within a local neighbourhood. A coherence index is proposed which may be used to select an appropriate neighbourhood for this smoothing procedure. The effects of smoothing on the uniformity of the classes with respect to the variables used to define them may be measured by Wilks's criterion, and examination of the class means. The method is demonstrated on a multi-variate data set.