NCP: Neighborhood-Preserving Non-Uniform Circle Packing for Visualization
🤖 AI Summary
This work addresses the challenge in visualization of simultaneously preserving data neighborhood relationships while encoding quantitative attributes via circle radii. The authors propose a non-uniform circular layout method grounded in circle packing theory, which uniquely formulates the joint objectives of neighborhood preservation and variable-radius encoding as a planar graph embedding problem. By leveraging non-convex optimization combined with a continuation method, the approach achieves a coherent representation that balances structural similarity and attribute magnitude. Experimental evaluations and two case studies demonstrate that the method efficiently produces high-quality, non-uniform circle packings that maintain neighborhood fidelity, thereby effectively supporting integrated analysis of data similarity and associated quantitative attributes.
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
circle packing
neighborhood preservation
non-uniform circles
visualization
quantitative attribute
Innovation
Methods, ideas, or system contributions that make the work stand out.
circle packing
neighborhood preservation
non-uniform visualization
planar graph embedding
continuation method
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