Spatial and semantic dimensions of landscape heterogeneity

This paper addresses the challenge of measuring spatial heterogeneity in categorical map data. Spatial heterogeneity is a complex notion that involves both spatial variability and attribute variability, and metrics to capture this are a product of their developers’ simplifying assumptions about both spatial and attribute dimensions. We argue that the predominantly binary treatment of categorical data is frequently an unnecessary oversimplification that can be replaced by ordered measures based on semantic similarity evaluations. We develop a typology of autocorrelation metrics for categorical data that identifies a critical gap: existing measures are limited in their ability to capture variability of both spatial and attribute dimensions simultaneously. We demonstrate an approach to formally characterize the semantic similarity between pairs of categorical data classes as a continuous numeric variable. A series of experiments on synthetic and actual land cover data contrasts the information content provided by metrics representative of all portions of the typology: the recently proposed semantic variogram, the indicator variogram, the contagion index, and the edge contrast index. Experimental results suggest that the typology captures essential qualities of metric information richness. Among our findings is that the commonly used contagion index is directly correlated with Moran’s I for 2-class maps but it fails to distinguish between negatively and positively autocorrelated patterns. We identify the semantic variogram as the only metric that can simultaneously detect both spatial and semantic attribute aspects of categorical autocorrelation. The semantic variogram is also relatively robust to attribute scale changes and therefore less sensitive to class aggregation than the other metrics.