The State of the Art in Cartograms

Cartograms combine statistical and geographical information in thematic maps, where areas of geographical regions (e.g., countries, states) are scaled in proportion to some statistic (e.g., population, income). Cartograms make it possible to gain insight into patterns and trends in the world around us and have been very popular visualizations for geo-referenced data for over a century. This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms. A particular focus is the study of the major cartogram dimensions: statistical accuracy, geographical accuracy, and topological accuracy. We review the history of cartograms, describe the algorithms for generating them, and consider task taxonomies. We also review quantitative and qualitative evaluations, and we use these to arrive at design guidelines and research challenges

Optimization-Based Construction of Quadrilateral Table Cartograms

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

Evaluating Cartogram Effectiveness

Cartograms are maps in which areas of geographic regions (countries, states) appear in proportion to some variable of interest (population, income). Cartograms are popular visualizations for geo-referenced data that have been used for over a century and that make it possible to gain insight into patterns and trends in the world around us. Despite the popularity of cartograms and the large number of cartogram types, there are few studies evaluating the effectiveness of cartograms in conveying information. Based on a recent task taxonomy for cartograms, we evaluate four major different types of cartograms: contiguous, non-contiguous, rectangular, and Dorling cartograms. Specifically, we evaluate the effectiveness of these cartograms by quantitative performance analysis, as well as by subjective preferences. We analyze the results of our study in the context of some prevailing assumptions in the literature of cartography and cognitive science. Finally, we make recommendations for the use of different types of cartograms for different tasks and settings

Computing Fast and Scalable Table Cartograms for Large Tables

Given an m x n table T of positive weights and a rectangle R with an area equal to the sum of the weights, a table cartogram computes a partition of R into m x n convex quadrilateral faces such that each face has the same adjacencies as its corresponding cell in T, and has an area equal to the cell's weight. In this thesis, we explored different table cartogram algorithms for a large table with thousands of cells and investigated the potential applications of large table cartograms. We implemented Evans et al.'s table cartogram algorithm that guarantees zero area error and adapted a diffusion-based cartographic transformation approach, FastFlow, to produce large table cartograms. We introduced a constraint optimization-based table cartogram generation technique, TCarto, leveraging the concept of force-directed layout. We implemented TCarto with column-based and quadtree-based parallelization to compute table cartograms for table with thousands of cells. We presented several potential applications of large table cartograms to create the diagrammatic representations in various real-life scenarios, e.g., for analyzing spatial correlations between geospatial variables, understanding clusters and densities in scatterplots, and creating visual effects in images (i.e., expanding illumination, mosaic art effect). We presented an empirical comparison among these three table cartogram techniques with two different real-life datasets: a meteorological weather dataset and a US State-to-State migration flow dataset. FastFlow and TCarto both performed well on the weather data table. However, for US State-to-State migration flow data, where the table contained many local optima with high value differences among adjacent cells, FastFlow generated concave quadrilateral faces. We also investigated some potential relationships among different measurement metrics such as cartographic error (accuracy), the average aspect ratio (the readability of the visualization), computational speed, and the grid size of the table. Furthermore, we augmented our proposed TCarto with angle constraint to enhance the readability of the visualization, conceding some cartographic error, and also inspected the potential relationship of the restricted angles with the accuracy and the readability of the visualization. In the output of the angle constrained TCarto algorithm on US State-to-State migration dataset, it was difficult to identify the rows and columns for a cell upto 20 degree angle constraint, but appeared to be identifiable for more than 40 degree angle constraint

Techniques for Statistical Data Visualization in GIS

This paper proposes an original solution to present statistical data using the facilities provided by the Geographical Information Systems, to improve the means of statistical data figure and distribution inside the territorial profile. The proposed solution allows to represent more statistical data sets, on the same map, using two different methods of data representation: using a color ramp to represent the territorial distribution of an aggregate indicator and a set of charts overlapped to represent the proportions of the variables that form the indicator. On the other hand, there is a way to represent statistical data using 3D cartograms. Thus, in GIS, the users can distinguish the intensity of the studied economic or social phenomenon because of the heights of the administrative units will be different.Geographical Information Systems, Spatial Visualization, ArcObjects, 2D and 3D Cartograms

Maps of Organic Agriculture in Australia

Australia is the world leader in organic agriculture, based on certified organic hectares. This has been the case since global organic statistics were first published (in 2000). Australia now accounts for more than half of the world’s certified organic hectares (54%). Australia has 35,645,000 certified organic hectares which is 8.8% of Australia’s agricultural land. In the present paper, three maps (cartograms, ‘maps with attitude’) of organic agriculture in Australia are presented. These three maps illustrate the data, at the state and territory level, for (a) certified organic hectares (35,645,037 hectares) (b) certified organic producers (n = 1,998), and (c) certified organic operators (producers + handlers + processors) (n = 4,028). States and territories are resized according to their measure for each attribute. The base-map for Australia, with states and territories coloured according to their state colours (or a variation thereof), is the standard cartographic representation of the country. The three organics maps are density-equalising cartograms (area cartograms) where equal areas on the map represent equal measures (densities) of the parameter under consideration. This mapping protocol creates distorted yet recognisable new maps that reveal where there is a high presence of the parameter under consideration (and the state or territory is ‘fat’), or a low presence (and the state or territory is ‘skinny’). These three maps visually reveal the uneven distribution of the metrics of organics across Australia, and, on a state by state basis, they suggest unrealised opportunities and potentials

Geographical information systems technologies for spatial visualization of statistical data

This paper proposes an original solution to present statistical data using the facilities provided by the Geographical Information Systems, to improve the means of statistical data figure and distribution inside the territorial profile. The proposed solution allows to represent more statistical data sets, on the same map, using two different methods of data representation: using a color ramp to represent the territorial distribution of an aggregate indicator and a set of charts overlapped to represent the proportions of the variables that form the indicator.Geographical Information Systems, Spatial Visualization, ArcObjects, Cartograms

Density-equalizing maps for simply-connected open surfaces

In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing flattening maps with any prescribed density distribution. By varying the initial density distribution, a large variety of mappings with different properties can be achieved. For instance, area-preserving parameterizations of simply-connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored

The Geography of Scientific Productivity: Scaling in U.S. Computer Science

Here we extract the geographical addresses of authors in the Citeseer database of computer science papers. We show that the productivity of research centres in the United States follows a power-law regime, apart from the most productive centres for which we do not have enough data to reach definite conclusions. To investigate the spatial distribution of computer science research centres in the United States, we compute the two-point correlation function of the spatial point process and show that the observed power-laws do not disappear even when we change the physical representation from geographical space to cartogram space. Our work suggests that the effect of physical location poses a challenge to ongoing efforts to develop realistic models of scientific productivity. We propose that the introduction of a fine scale geography may lead to more sophisticated indicators of scientific output.Comment: 6 pages, 3 figures; minor change