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. © 2024 China Ship Scientific Research Center. All rights reserved.