## Choropleth color scales for modifiable areal units

ISBN 978-85-88783-11-9

### Authors

^{1}Samsonov, T.

### Abstract

Choropleth maps are usually used for display of relative parameters per territorial units. Many automatic classification methods exist for data classification (Slocum et al. 2008). Sequential and diverging scales could be used for choropleth representation (Brewer 2005). In contrast to data classification, selection of colors for choropleth mapping is weakly automated. In this paper we investigated the problem of choropleth color scale modification when the areal unit can be changed. This situation is typical for multiscale statistical mapping when the data is visualized on several levels of detail, each depicting the most corresponding subdivision of administrative hierarchy. Multiscale maps help the reader to investigate the changes that occur when the scale of observation and mapping units is modified. This means that symbols across scales should be comparable, and the reader should be protected from misinterpretation of symbols. In case of choropleth mapping the changes in color scale should reflect the changes in statistical distribution between levels of detail. Theoretically, the highest level of visual comparability could be achieved if the same classification and color scale is used for all levels of detail. However, this possibility is extremely rare in practice, because statistical distributions differ significantly. In our research we concentrated on modification of one-hue sequential color scales (only saturation is modified) according to the range of the data. At the initial stage the user selects color scale he wants to use. Our first idea was to associate it with the range of the data between minimum (Vmin) and maximum (Vmax) value across all levels of detail. Then the colors for every level can be simply picked from this color gradient. However, this simple approach can lead to non-vivid representation if the range becomes too narrow and covers only a short fragment of color gradient with faintly distinguishable colors. From the other side, application of the one color scale for all levels of detail is even more incorrect, because the reader will conclude that data distributions are similar. Guided by these considerations we developed a compromise methodology of adaptive range transformation for selection of colors from one-hue color scale. For this we use global Vmin and Vmax and also minimum (vmin) and maximum (vmax) values at current level of detail (we call them local). Then the transformed value for local minimum is calculated as Vmin*(vmin/Vmin)^r, where “^” means power operation and r is the factor between 0 and 1 that reflects the sensitivity of the transformation to the difference between local and global minima. Corrected maximum value is calculated similarly as Vmax*(vmax/Vmax)^r. When r = 0 the range is stretched towards the full scale, and for r = 1 the range is not stretched at all. The transformed data range is used only for selection of colors and not in classification of the data. Values for intermediate class breaks are transformed similarly to pick the colors from gradient. We applied this approach on various statistics from USA Census and EU NUTS data sources. Range transformation helped us to achieve an optimal balance between demonstrating the changes in data range (narrowing, widening and biasing) and making representation vivid enough. This means that if data range becomes narrower the image becomes less contrasting but not in linear proportion with data range due to application of sensitivity factor r. Our future investigations will be directed to multicolor gradients, conducting a survey among users to test the reliability of the methodology, and extending it to more general cases of modifiable areal units. References Brewer CA (2005) Designing better maps. A guide for GIS users (First edit.). Redlands: ESRI Press, 2005. Slocum TA, McMaster RB, Kessler FC, & Howard HH (2008) Thematic Cartography and Geovisualization (3rd Editio., p. 576). New York: Prentice Hall

### Keywords

Choropleths; Colors; Modifiable areal unit problem

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