A Game Theoretic Approach for Simultaneous Compaction and Equipartitioning of Spatial Data Sets

Data and object clustering techniques are used in a wide variety of scientific applications such as biology, pattern recognition, information systems, etc. Traditionally, clustering methods have focused on optimizing a single metric, however, several multidisciplinary applications such as robot team deployment, ad hoc networks, facility location, etc., require the simultaneous examination of multiple metrics during clustering. In this paper, we propose a novel approach for spatial data clustering based on the concepts of microeconomic theory, which can simultaneously optimize both the compaction and the equipartitioning objectives. The algorithm models a multistep, normal form game consisting of randomly initialized clusters as players that compete for the allocation of data objects from resource locations. A Nash-equilibrium-based methodology is used to derive solutions that are socially fair for all the players. After each step, the clusters are updated using the KMeans algorithm, and the process is repeated until the stopping criteria are satisfied. Extensive simulations were performed on several real data sets as well as artificially synthesized data sets to evaluate the efficacy of the algorithm. Experimental results indicate that the proposed algorithm yields significantly better results as compared to the traditional algorithms. Further, the proposed algorithm yields a high value of fairness, a metric that indicates the quality of the solution in terms of simultaneous optimization of the objectives. Also, the sensitivity of the various design parameters on the performance of our algorithm is analyzed and reported.