A new construction method for circle cartograms

An area cartogram is a transformed map on which areas of regions are proportional to statistical data values; it is considered to be a powerful tool for the visual representation of statistical data. A circle cartogram is a type of area cartograms, on which regions are represented by circles. Its first construction algorithm is proposed by Dorling in 1996, based on the following requirements to construct visually elegant cartograms: 1) maintain the similarity of configurations between circles and regions, 2) express the contiguity of regions on cartograms if possible, and 3) avoid overlap of circles. The algorithm is widely used for its easiness to use and its ability to express a spatial distribution of data; however, the relative positions of circles on cartograms sometimes greatly differ from the geographical maps, since the algorithm does not consider the first requirements explicitly. In this paper, it is first pointed out that the construction problem of circle cartograms resembles that of distance cartograms, and the only difference is the existence of third requirement. Then a new construction method for circle cartograms is proposed based on the distance cartogram construction method; the proposed method is formulated as non-linear minimization with inequality constraint conditions. Finally its applicability is confirmed using dataset, including the comparison with the result of previous algorithm.