Optimization-Based Construction of Quadrilateral Table Cartograms

Ryo Inoue,Mao Li

doi:10.3390/ijgi9010043

Abstract

A quadrilateral table cartogram is a rectangle-shaped figure that visualizes table-form data; quadrilateral cells in a table cartogram are transformed to express the magnitude of positive weights by their areas, while maintaining the adjacency of cells in the original table. However, the previous construction method is difficult to implement because it consists of multiple operations that do not have a unique solution and require complex settings to obtain the desired outputs. In this article, we propose a new construction for quadrilateral table cartograms by recasting the construction as an optimization problem. The proposed method is formulated as a simple minimization problem to achieve mathematical clarity. It can generate quadrilateral table cartograms with smaller deformation of rows and columns, thereby aiding readers to recognize the correspondence between table cartograms and original tables. In addition, we also propose a means of sorting rows and/or columns prior to the construction of table cartograms to reduce excess shape deformation. Applications of the proposed method confirm its capability to output table cartograms that clearly visualize the characteristics of datasets.

Highlights

A contiguous area cartogram is a visualization method for geospatial data that records the attributes of positive values of regions, such as population and Gross Domestic Product (GDP)
We proposed a method to construct quadrilateral table cartograms from the given table-form data, along with a method to sort rows and columns of tables, to output table cartograms with small deformations
The proposed method for the construction consists of two steps: the first step adjusts the heights of rows and widths of columns of tables by preserving the direction of horizontal and vertical edges; the second step transforms the shapes of cells to fit their sizes to their given data values, while controlling the degrees of deformation

Summary

Introduction

A contiguous (or continuous) area cartogram is a visualization method for geospatial data that records the attributes of positive values of regions, such as population and Gross Domestic Product (GDP). It is a deformed map in which the shape of each region is transformed to fit its area on the cartogram to its size of positive attribute value, while maintaining the adjacency of regions (see [1,2]). The special feature of visualization by contiguous area cartograms is the data representation through the deformation of figures This feature is effective for geospatial datasets and for table-form datasets with positive values. The most common examples of table cartograms are the visualization of characteristics of elements on the periodic chemical table, the table cartograms that exhibit several features of elements created [3,4,5], and a table cartogram published by the European Chemical Society published in 2019, International Year of the Periodic Table of Chemical Elements, to exhibit the quantity of chemical elements on Earth [6]

Methods

Results

Discussion

Conclusion