A generalized cross‐tabulation matrix to compare soft‐classified maps at multiple resolutions

This paper addresses two grand challenges in the development of methods for Geographic Information Science (GIS). First, this paper presents techniques to compute a cross‐tabulation matrix for soft‐classified pixels. Second, it shows how to compute the cross‐tabulation matrix at multiple scales. The traditional approach to construct the cross‐tabulation matrix uses a Boolean operator to analyse pixels that are hard‐classified. For soft‐classified pixels, the contemporary approach uses a Multiplication operator; the fuzzy approach uses a Minimum operator; whereas this paper proposes a multiple‐resolution approach that uses a Composite operator. There are difficulties with the traditional, contemporary, and fuzzy methods of computing the cross‐tabulation matrix. The proposed multiple‐resolution method resolves those difficulties. Furthermore, the proposed method facilitates multiple‐resolution analysis, so it can examine how results change as a function of scale. The paper derives the equations to compute cross‐tabulation matrices at multiple resolutions and connects those equations to ontological foundations of GIS.