A microeconomic approach to multi-objective spatial clustering

Application of clustering approaches in cross-disciplinary domains has necessitated the identification of new methods capable of simultaneous examination of multiple conflicting metrics during optimization. In this work, we propose a novel multi-objective clustering approach based on the concepts of microeconomic theory. In a multi-step, normal form game theoretic setup, each randomly initialized cluster is categorized as either a player or a resource in the game. The players in the game compete against each other for allocation of resources, and try to maximize their own utilities. The utility for a strategy of a player is a function of the clustering objectives. A Nash equilibrium based methodology is used to identify a solution that is socially fair. The algorithm is tested on real as well as artificially synthesized spatial data sets to evaluate the efficacy of the algorithm, and the quantitative measure of the quality of clusters in terms of fairness.