Quantitative visualizations of hierarchically organized data in a geographic context

Here we introduce a novel quantitative technique for visualizing hierarchically organized data in a geographic context. In contrast to existing techniques, our visualization emphasizes the hierarchical relationships in the data by depicting them in a standard tree format that takes advantage of many fundamental perceptual properties. Our technique allows users to define a geographic axis and visualize how well a tree correlates with the ordering of geographical locations along this axis. This is accomplished by finding the ordering of leaf nodes, subject to the constraints of the tree topology, which minimizes the number of crossings that occur between lines that connect leaf nodes to their associated geographic locations. In this optimal layout, any crossings that occur between these lines indicate discordance between the topology of the tree and the user defined geographic axis. We have developed a branch-and-bound algorithm that allows optimal leaf orderings to be determined quickly enough to support interactive exploration of different geographic axes even for large multifurcating hierarchies. The quantitative nature of our visualization has allowed us to specify a permutation test for determining if the relationship between a tree topology and a geographic axis is statistically significant. In this paper, the utility of our visualization is demonstrated on biological data sets, but our method is applicable to any hierarchical data where geographic structure may be of interest.