Neighborhood-Preserving Voronoi Treemaps

TL;DR

This paper introduces a novel Voronoi treemap algorithm that preserves data neighborhood relationships by integrating similarity measures into layout generation, improving the visualization of hierarchical and attribute-based data.

Contribution

The authors extend Voronoi treemaps to incorporate data similarity, enabling neighborhood preservation alongside hierarchical representation.

Findings

Effective neighborhood preservation demonstrated on real-world data

Improved treemap metrics compared to traditional methods

Versatile application in infographics and linguistics

Abstract

Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples include geographical attributes like shared borders between countries or contextualized semantic information such as embedding vectors derived from large language models. In this work, we introduce a Voronoi treemap algorithm that leverages data similarity to generate neighborhood-preserving treemaps. First, we extend the treemap layout pipeline to consider similarity during data preprocessing. We then use a Kuhn-Munkres matching of similarities to centroidal Voronoi tessellation (CVT) cells to create initial Voronoi diagrams with equal cell sizes for each level. Greedy swapping is used to improve the neighborhoods of cells to match the data's similarity further. During optimization, cell areas are iteratively adjusted to their respective sizes while preserving the existing neighborhoods. We demonstrate the practicality of our approach through multiple real-world examples drawn from infographics and linguistics. To quantitatively assess the resulting treemaps, we employ treemap metrics and measure neighborhood preservation.