Neighborhood-Preserving Voronoi Treemaps

Area of Science:

• Data Visualization
• Computational Geometry
• Information Visualization

Background:

• Voronoi treemaps visualize hierarchical data but often overlook non-hierarchical data attributes like similarity.
• Existing methods do not effectively represent complex relationships such as geographical proximity or semantic similarity.

Purpose of the Study:

• To develop a novel Voronoi treemap algorithm that integrates data similarity into the layout process.
• To generate treemaps that preserve data neighborhoods while accurately reflecting hierarchical structures and similarity metrics.

Main Methods:

• Extended the treemap layout pipeline to include similarity-based data preprocessing.
• Utilized Kuhn-Munkres matching to align data similarities with centroidal Voronoi tessellation (CVT) cells.
• Employed greedy swapping and iterative area adjustment to optimize neighborhood preservation and cell sizing.

Main Results:

• Developed a practical algorithm for generating similarity-aware Voronoi treemaps.
• Demonstrated effectiveness using real-world examples from infographics and linguistics.
• Quantitatively validated neighborhood preservation using established treemap metrics.

Conclusions:

• The proposed algorithm successfully generates Voronoi treemaps that preserve data neighborhoods by leveraging similarity.
• This approach offers a significant advancement in visualizing complex datasets with both hierarchical and similarity-based attributes.
• The method provides a powerful tool for data analysis and presentation in diverse fields.