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Open AccessArticle

Optimization-Based Construction of Quadrilateral Table Cartograms

by Ryo Inoue * and Mao Li
Department of Human-Social Information Sciences, Graduate School of Information Sciences, Tohoku University, Miyagi 980-8577, Japan
*
Author to whom correspondence should be addressed.
ISPRS Int. J. Geo-Inf. 2020, 9(1), 43; https://doi.org/10.3390/ijgi9010043
Received: 20 December 2019 / Revised: 20 December 2019 / Accepted: 13 January 2020 / Published: 14 January 2020
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.
Keywords: quadrilateral table cartogram; contiguous area cartogram; visualization; table-form data; optimization quadrilateral table cartogram; contiguous area cartogram; visualization; table-form data; optimization
MDPI and ACS Style

Inoue, R.; Li, M. Optimization-Based Construction of Quadrilateral Table Cartograms. ISPRS Int. J. Geo-Inf. 2020, 9, 43.

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