Categorical mapping and error modeling based on the discriminant space

Abstract

Despite developments in error analysis for discrete objects and interval/ratio fields, there exist conceptual problems with the case of nominal fields. This paper seeks to consolidate a conceptual framework based on the discriminant space for categorical mapping and error modeling. The discriminant space is defined upon the essential properties and processes underlying occurrences of spatial classes, and lends itself to geostatistical analysis and modeling. The discriminant space furnishes consistency in categorical mapping by imposing class-conditional mean structures that are associated with discriminant or "environmental" variables in various statistical models, and facilitates physically interpretable and scale-dependent error modeling. Further research will focus on models and methods based on multi-dimensional discriminant space and at multiple scales.