Applying Cooperative Games with Coalition Structure for Data Clustering

Abstract

This paper considers a cooperative game in which the distance (or similarity) between some objects (players) can be measured numerically. For this game, a characteristic function is defined so that it takes high values for the coalitions consisting of most close (similar) players in comparison with the players from the other coalitions. Such a function does not satisfy superadditivity, and hence it seems reasonable to introduce the model with coalition structure. Therefore, this game can be treated as a clustering procedure for objects (players). Finally, the existence conditions of a stable coalition structure are established, which allow to perform efficient (crisp) clustering.