Comparison of thematic maps using symbolic entropy

Abstract

Comparison of thematic maps is an important task in a number of disciplines. Map comparison has traditionally been conducted using cell-by-cell agreement indicators. More recently, other methods have been proposed that take into account not only spatially coincident cells in two maps, but also their surroundings or the spatial structure of their differences. The objective of this article is to propose a framework for map comparison that considers (1) the patterns of spatial association in two maps, in other words, the map elements in their surroundings; (2) the equivalence of those patterns; and (3) the independence of patterns between maps. Two new statistics for the spatial analysis of qualitative data are introduced that are based on the symbolic entropy of the maps. As well, all inferential elements to conduct hypothesis testing are developed. The framework is illustrated using real and simulated maps.

Keywords:

• thematic maps
• map comparison
• qualitative variables
• spatial association
• symbolic entropy
• hypothesis testing

Acknowledgments

The authors gratefully acknowledge the feedback of five anonymous reviewers who commented on two early versions of this article. Manuel Ruiz Marín was partially supported by MCINN (Ministerio de Ciencia e Innovación) grant MTM2009-07373, Fundación Séneca of Región de Murcia, and by grant 861–2009–2010 from the Social Sciences and Humanities Research Council of Canada. Fernando López received financial support from project ECO-2009-10534-ECON of Ministerio de Ciencia y Tecnología and from project 11897/PHCS/09 of Fundación Séneca de la Región de Murcia.

Notes

1. http://geogratis.cgdi.gc.ca/CLI/index_agriculture.html.

2. Matlab code and a stand-alone application that implements the statistics are available, along with the maps used in the illustration, at: http://www.science.mcmaster.ca/geo/faculty/paez/publications.html.