NCP: Neighborhood-preserving non-uniform circle packing for visualization

Circle packing is widely used in visualization due to its aesthetic appeal and simplicity, particularly in tasks where the spatial arrangement and relationships between data are of interest, such as understanding proximity relationships (e.g., images with categories) or analyzing quantitative data (e.g., housing prices). Many applications require preserving neighborhood relationships while encoding a quantitative attribute using radii for data analysis. To meet these two requirements simultaneously, we present a neighborhood-preserving non-uniform circle packing method, NCP. This method preserves neighborhood relationships between the data represented by non-uniform circles to comprehensively analyze similar data and an attribute of interest. We formulate neighborhood-preserving non-uniform circle packing as a planar graph embedding problem based on the circle packing theorem. This formulation leads to a non-convex optimization problem, which can be solved by the continuation method. We conduct a quantitative evaluation and present two use cases to demonstrate that our NCP method can effectively generate non-uniform circle packing results.