Information Space Partitioning Using Adaptive Voronoi Diagrams

Abstract

In this paper, we present and evaluate a Voronoi method for partitioning continuous information spaces. We define the formal characteristics of the problem and discuss several well-known partitioning methods and approaches. We submit that although they all partially solve the problem, they all have shortcomings. As an alternative, we offer an approach based on an adaptive version of the multiplicatively weighted Voronoi diagram. The diagram is ‘adaptive’ because it is computed backwards; that is, the generators' weights are treated as dependent rather than independent variables. We successfully test this adaptive solution using both ideal-typical (artificial) and empirical data. Since the resultant visualizations are meant to be used by human subjects, we then discuss the results of a usability experiment, positioning the adaptive solution against a commonly used rectangular solution and the classic nonweighted Voronoi solution. The results indicate that in terms of usability, both the rectangular and the adaptive Voronoi solution outperform the standard Voronoi solution. In addition, although subjects are better able to gage rectangular area relationships, only the adaptive Voronoi solution satisfies all geometric constraints of weight-proportional partitioning.