A conceptual framework for categorical mapping and error modeling

Despite developments in error modeling in discrete objects and continuous fields, there exist substantial conceptual problems in the domain of nominal fields, which are largely unsolved with little consensus. This paper seeks to consolidate a conceptual framework for categorical information and uncertainty characterization. A conceptual framework is proposed on the basis of discriminant space, defined by essential properties or driving processes underlying occurrences of area-classes. Such a framework furnishes consistency in categorical mapping by imposing class-specific mean structures that can be regressed against discriminant variables, and facilitates scale-dependent error modeling that can effectively emulate the variation found among observers in terms of classes, boundary positions, numbers of polygons, and boundary network topology. Based on simulated data, comparisons between indicator Kriging-based stochastic simulation and Gaussian simulation confirmed the replicability of the discriminant space model for mapping the "mean" area-classes, reflecting mean responses of discriminant variables, and spatial uncertainty therein, mirroring spatially correlated residuals.