Quantifying the relationships between network distance and straight-line distance: applications in spatial bias correction

In many applications of spatial analysis methods, straight-line Euclidean distance (ED) is frequently used as the distance metric. However, ED is not adequate to reflect the actual distance between spatial objects and would probably lead to biased results. In order to understand the effects of using ED, this study estimates the quantitative relationships between ED and actual network distance (ND) across 25 Chinese cities and identifies their spatial variations using functional data analysis (FDA). The analysis is based on the detour index (DI), which is defined as the ratio of ND to ED. The results reveal significant linear relationships between ND and ED (with an average DI value of 1.324) across all selected cities. FDA further unveils the modes of the spatial variations of DI from short-distance to long-distance travel at the intra-city scale, showing that short-distance travels in a city usually require more detour than long-distance ones. Finally, we take K-function analysis as an example to demonstrate the usefulness of the estimated DI relationships to correct the bias of ED. Our experiments show that by applying the estimated DI relationships, the results of K-function analysis with ED can be substantially improved to become more realistic. We also suggest and evaluate a kNN based method to determine an appropriate DI value and adjust ED.