Weight-proportional Information Space Partitioning Using Adaptive Multiplicatively-Weighted Voronoi Diagrams

We define the spatial constraints and objective function for weight-proportional partitioning of information spaces. We evaluate existing methods in light of these definitions and find that none performs as desired. We then formulate an alternative approach based on an adaptive version of the multiplicatively weighted Voronoi diagram; i.e., the diagram’s weights are computed based on a set of predefined area relationships. We test this adaptive solution using various sets of ideal-typical data and find that it behaves well. Next, we evaluate users’ capabilities to properly estimate area relationships in this type of model. We compare the adaptively computed results with those from more traditional partitionings; i.e., a rectangular partitioning and an ordinary, straight-lined Voronoi diagram. Surprisingly, we find that the adaptive multiplicatively weighted diagram outperforms the ordinary Voronoi solution.