Range of Categorical Associations for Comparison of Maps with Mixed Pixels

This paper presents a method to compare maps that contain pixels that have partial membership to multiple categories, i.e., mixed or soft classified pixels. The method quantifies ranges for associations among categories based upon possible variations in sub-pixel spatial allocation. The paper derives the mathematical equations for constructing the range of associations based on three types of cross-tabulation matrices, the greatest matrix, the random matrix, and the least matrix. We demonstrate how the analysis can be combined with multiple resolution map comparison to specify the resolution at which clusters exist on a single map or between two maps. The method produces a range that reflects the amount of uncertainty in the categorical associations. We illustrate the procedure with both a simple example and data from the Plum Island Ecosystems study site in Massachusetts, USA.