On Objective-Based Clustering from the Perspective of Transportation Problem

The transportation problem is to determine the amount of transportation from a supply location to a demand location so as 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 a given multiple supply and demand locations. On the other hand, clustering based on objective function optimization (objective-based clustering), represented by hard c-means and fuzzy c-means methods, is the problem of determining the cluster center and membership degree so as to minimize the objective function consisting of dissimilarity between each data and the cluster centers and membership degree of data to a cluster for a given data set. There is a strong relevance between the two. In this paper, we discusses several objective function optimization-based clustering methods from the perspective of transportation problems, examines the relevance between them, and proposes and examines a new evaluation function.