利用Minkowski距离逼近道路网络距离算法研究

道路网络背景下的距离度量（如道路网络距离、旅行时间）是在空间分析或空间统计过程中常用的距离度量，但在科研过程中由于道路数据的可获得性和精度等方面的限制，该类距离的计算可能较为困难。Minkowski距离函数是欧氏空间中的广义距离函数，其参数p值的不同代表着对空间不同的度量。利用Minkowski的通用性和灵活性（参数p不同的取值），研究如何更好地逼近道路网络距离。同时，探索不同道路网络的部分计量特征（如密度、弯曲度等）与最优p值之间的关系。实验证明，相对于最常用的欧氏距离度量，优选p值后的Minkowski距离函数能够更大程度上逼近道路距离。而通过对道路网络计量特征与最优p值之间的关系的分析，指出了弯曲度与最优p值之间的对应关系，它对于p值的选择具有重要的指导意义。此外，为了验证Minkowski距离逼近算法的可行性，以地理加权回归分析为例，通过对比传统的欧氏距离度量、最优Minkowski距离度量和道路网络距离（旅行时间）对模型解算结果的影响，指出优选后Minkowski距离一定程度上更接近于采用旅行时间对模型解算的结果。

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.