A multivariate spatial structure indicator based on geographic similarity

Quantification of spatial structure reveals the distribution patterns of geographic features, which is essential for geographic analysis. For quantitative measurements of multivariate spatial structure, existing methods often neglect either the geographic meaning or the spatial combination of the multivariate dataset. In this paper, a new indicator for multivariate spatial structure (MuSS) is proposed. Since multivariate datasets characterize geographic conditions, the correlation between multivariate attributes at different locations can be measured as the similarity of geographic conditions. The MuSS indicator evaluates whether location pairs with closer distances have higher geographic similarities. Experimental results show that MuSS outperforms existing methods in differentiate multivariate datasets with varied spatial distribution patterns. A MuSS value deviating from 1 suggests that geographic similarity between location pairs is relevant to their distance, and the statistical significance of the captured distribution patterns is evaluated using a p-value from a permutation test. MuSS is also applied to real geographic data at different spatial resolutions in two study areas with diverse distribution patterns. Case studies show that MuSS provides consistent comparison results for spatial structure levels between study areas, while existing methods cannot.