A new construction method for circle cartograms and its application

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. One of the most familiar cartograms is a circle (or circular) cartogram, on which regions are represented by circles. Dorling first proposed a circle cartogram construction algorithm in 1996 according to the requirements avoid overlap of circles' and keep contiguity of regions as much as possible'. The algorithm first places circles according to the geographical configuration of regions and then moves them one by one in order to fulfil the requirements. It outputs results which express a spatial distribution of data; however, the relative positions of circles on cartograms sometimes greatly differ from the geographical maps. Cartogram readers usually compare the shape of cartograms to that of geographical maps, realize the shape distortion, and recognize the characteristics of spatial distribution of represented data on cartograms; removing the excess circle reposition process from the algorithm is preferable to make the relative position of circles on resultant cartograms as similar as possible to that on the geographical map. In this paper, I propose a new construction method for circle cartograms that attaches a high value to the preservation of relative position of circles while considering the requirements proposed by Dorling. I formulated a construction problem for non-linear minimization with inequality constraint conditions and applied the method to the world population dataset.