设施选址对提高居民生活质量至关重要,利用地理可达相似性聚类对空间元素进行分类是求解此类问题的重要方法.然而,现有的应用于地理可达性分析的聚类算法存在地理可达性测度不准确、不涉及簇中心选取或簇中心不可达等缺陷,不能有效求解真实场景下的设施选址问题.基于此,本文提出一种基于可达距离的模糊C均值聚类算法(Fuzzy C-Means based on Reachable Distance,FCM-RD).FCM-RD算法改造了经典FCM算法的目标函数、隶属度函数和簇中心函数,使其适用基于可达距离的聚类分析.其次,以沿路网的最短路径距离作为可达距离衡量元素间的地理可达相似性,将聚类元素的二维地理坐标映射为路网坐标,并以此设计簇中心迭代机制,实现在聚类过程中以可达距离迭代不受约束的可达簇中心.同时,对所提簇中心迭代机制的有效性进行理论分析和实验验证,结果表明,FCM-RD算法在每次迭代中所选的各簇簇中心唯一且为当前簇类目标函数最小值点.最后,基于真实地理场景的仿真实验表明,相比基准算法,FCM-RD不仅能获得位置不受限的可达簇中心,而且能获得更好的聚类效果,为实际场景下的地理空间聚类方案提供了有效且精准的解决方案.
A Fuzzy C-Means Clustering Algorithm Based on Reachable Distance
Facility location is of great significance for improving residents'quality of life,and geographic accessibility indicators,such as the road network,are often used as the main decision-making factors.Clustering analysis based on geographic accessibility is an important tool for solving such problems.However,existing clustering algorithms often fail to guarantee the accuracy of clustering results,the accessibility of cluster centers,or the selectivity of cluster centers,making them less effective in solving the facility location problem in real scenarios.This paper proposes a Fuzzy C-Means clustering algorithm based on Reachable Distance(FCM-RD),which modifies the objective function,the membership function,and the cluster center function of the classical FCM.It employs reachable distance as a measure of geographic reachable similarity and iterates the cluster centers during the clustering process.Specifically,to capture the true relationships and connectivity between different elements,FCM-RD takes into account physical and spatial barriers,employs the shortest path distance along the road network as the reachable distance,and aligns geographic coordinates with the road network.It is possible for one position on the road network to correspond to multiple positions in geographic coordinates.Consequently,when multiple candidate positions for cluster centers are obtained,a cluster center correction mechanism is designed to iterate the accessible cluster center with reachable distance during the clustering process.Mathematical analysis and experiments in actual scenarios both show the validity of the cluster center iteration mechanism,showing the selected cluster centers in each iteration of FCM-RD are the unique and minimum value points of the intra-cluster objective function.The rationality of FCM-RD is further verified through experiments,and it is compared with baseline algorithms from three aspects:experimental results,convergence,and performance.The results indicate that,compared to the baseline algorithms,FCM-RD improves performance on both the mean and maximum indicators of the shortest reachable distance,with some indicators even improving by up to 38.9%.In a few experiments,there are slight improvements in the DB index and silhouette coefficient indicators,and 100%of the cluster centers selected by FCM-RD are located on the road network.FCM-RD overcomes the shortcomings of ignoring geographical obstacles and unreachable cluster centers.In conclusion,FCM-RD not only obtains accessible cluster centers without location restrictions but also achieves better clustering results.FCM-RD provides an effective and precise solution for geographical spatial clustering in practical scenarios.
万方数据
维普
