Optimized Spatial Clustering for Target Finding and Maximum Effects

Spatial clustering is the process of grouping a set of spatial objects so that objects within the same group have high similarity. In the context of GIS, similar objects in a cluster share certain common characteristics such as proximity and "importance\´ in relation to some purpose. We consider a special case of "spatial groups" pertaining to a common purpose in this paper. Given the data that have different densities distributed over a geographical area, how unique groups could be formed over them in order to maximize the total coverage by these groups. By maximizing the coverage, applications could be either destructive or constructive by intension, e.g. a jet fighter pilot needs to make a real-time critical decision at a split of second to locate several separate targets to hit in order to cause maximum damage, when it flies over an enemy terrain, a town planner is considering where to station certain resources (sites for schools and hospitals, security patrol routes, air-born food ration drops for humanitarian aid, etc.) for maximum effect, given a vast area of different distribution of densities for benevolent purposes. An optimized grouping algorithm developed by the authors in linear programming is compared with classical K-means, over two different case studies in this paper.