Algorithm of Approximating Road Network Distance Via the Minkowski Distance

The distance metrics under a network context such as road network distance, and travel time measurement have been commonly applied in the domains of spatial analysis and spatial statistics. In practice; however, it might be difficult to calculate these metrics properly due to the limits of data accessibility and accuracy problems. The Minkowski distance function is a generalized distance metric in the Euclidean space, and it may present various kinds of metrics when different values of the power parameter p are specified. In this article, we use the Minkowski distance function to approximate the road network distance taking advantage of its generality and flexibility. We also explored the relationships between the varying optimal values of p and a set of quantitative characteristics including road network density, curvature, etc. in accordance with road networks of distinct features. The results show that network distance could be approximated better by the Minkowski distance with an optimized power parameter p than Euclidean distance, i.e. straight line distance. In addition, the optimum value of pcanbe affected largely by the curvature of a road network, which might provide an important clue for selectingMinkowski distance for approximation. We take the geographical weighted regression (GWR) technique as an example, and calibrate a GWR model with Euclidean distance, and Minkowski distance with an optimal power value p and travel time, respectively. The results show that the estimates with the optimal Minkowski distance provided closer coefficient estimates to the values calibrated with travel time than those from the calibration using Euclidean distance.