PowerHierarchy: visualization approach of hierarchical data via power diagram

Voronoi treemaps are widely used for hierarchical data visualization. Existing methods calculate the visualization layouts of hierarchical data by combining the proportion optimization of weights and Lloyd's method of sites. However, this may not only produce results with large area errors but also require more time consumption. Besides, the relative visualization position of the same data element between adjacent frames in dynamic hierarchical data may be changed abruptly, resulting in unclear visual results. To this end, we propose an efficient and topological structure preserved visualization approach, called PowerHierarchy, for visualizing hierarchical data. Firstly, an improved version of the power diagram computing algorithm is introduced to generate the visualization layouts of each data element in the hierarchy. Unlike random initialization, we construct a centroidal Voronoi tessellation as input and then use a Breadth-First traversing strategy to adapt the depth information to produce visual layouts of static hierarchical data. Based on this, an updating scheme is presented for visualizing dynamic hierarchical data, where previous results are iteratively fed as inputs to initialize current layouts. Besides, the external boundary sites and their subsites are projected onto the visual boundary and then moved into the visual region with the relative position preserved. Experimental results on several datasets demonstrate the efficiency, accuracy, and topology preservation advantage of our proposed visualization approach.