Automatic Polygon Layout for Primal-Dual Visualization of Hypergraphs

TL;DR

This paper introduces an automatic algorithm for generating polygon layouts to visualize N-ary relationships in hypergraphs, including dual and joint optimization views for enhanced data insight.

Contribution

The paper presents a novel optimization-based algorithm for automatic polygon layout generation and a dual visualization framework for hypergraph data analysis.

Findings

Effective automatic layout generation for N-ary relationships

Dual visualization reveals additional data insights

Joint optimization improves layout quality and interpretability

Abstract

N-ary relationships, which relate N entities where N is not necessarily two, can be visually represented as polygons whose vertices are the entities of the relationships. Manually generating a high-quality layout using this representation is labor-intensive. In this paper, we provide an automatic polygon layout generation algorithm for the visualization of N-ary relationships. At the core of our algorithm is a set of objective functions motivated by a number of design principles that we have identified. These objective functions are then used in an optimization framework that we develop to achieve high-quality layouts. Recognizing the duality between entities and relationships in the data, we provide a second visualization in which the roles of entities and relationships in the original data are reversed. This can lead to additional insight about the data. Furthermore, we enhance our framework for a joint optimization on the primal layout (original data) and the dual layout (where the roles of entities and relationships are reversed). This allows users to inspect their data using two complementary views. We apply our visualization approach to a number of datasets that include co-authorship data and social contact pattern data.