Objective-Based Clustering from the Perspective of Transportation Problems: Relevance and Proposal of a New Clustering Method

This paper discusses objective-based clustering, represented by hard -means and fuzzy c -means (FCM) methods, from two perspectives. The first is the relationship between transportation problems and objective-based clustering. The transportation problem involves determining the amount of transportation from a supply location to a demand location to minimize the total transportation cost, given the respective supply and demand quantities and the respective transportation costs from the supply location to the demand location for given multiple supply and demand locations. In this study, we demonstrate a theoretical connection between transportation problems and objective-based clustering. The second is the proposal of a new clustering method that focuses on the first argument. First, by focusing on the transportation problem, we discuss the problem of defuzzification in methods that introduce fuzzy concepts, including FCM, that is mainstream in objective-based clustering, and propose an index to evaluate the clustering results from the perspective of defuzzification. Subsequently, we propose a new clustering algorithm based on this index. Moreover, we evaluate the performance of the proposed method using numerical examples.