On Objective-Based Clustering from the Perspective of Transportation Problem II

Abstract

The transportation problem is the problem of determining the amount of transportation from a supply location to a demand location so as to minimise the total transportation cost, given a given number of supply and demand locations, the amount of transportation from each supply location to the demand location, and the transportation cost according to the distance from the supply location to the demand location. On the other hand, clustering methods for unsupervised division of given data into a given number of clusters can be broadly classified into hierarchical and non-hierarchical. The latter are referred to as ’objective-based clustering’ in this paper, as they generally search for the optimal solution of a set objective function under constraint conditions and obtain it as the clustering result. In the previous paper, several objective-based clustering methods from the perspective of transportation problems were discussed and the correlation between them was examined. Furthermore, based on these considerations, an index for evaluating clustering results was proposed. Based on the previous paper, this paper first discusses the evaluation functions for the clustering results proposed in the previous section through numerical examples. Next, a new objective-based clustering algorithm from the perspective of transportation problems is presented.