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Visual Analytics Using Density Equalizing Geographic Distortion

Visualizing large geo-demographical data sets using pixel-based techniques involves mapping the geo-spatial dimensions of a data point to screen coordinates and appropriately encoding its statistical value by color. Analysis of such data is a great challenge. General tasks involve clustering, categorization and searching for patterns of interest for sociological or economic research. Available visual encodings and screen space limitations lead to over-plotting and hiding of patterns and clusters in densely populated areas, while sparsely populated areas waste space and draw the attention away from areas of interest. In the current paper, two new approaches (RadialScale and AngularScale) are introduced to create density-equalized maps, while preserving recognizable features and neighborhoods in the visualization. The approaches apply a multi-scaling technique based on local features of the data described as local minima and maxima of point density. Consequently, scaling is conducted several times around these features, thus leading to more effective distortions. Results are applied and discussed on two applications. Evaluation shows to outperform traditional techniques for homogeneity of distortion and efficient use of space. 1 MOTIVATION Large point sets - as widely used to analyze geo-related demographic data - are nearly impossible for people to understand quickly by in- specting high resolution raw data. In the age of massive databases and consequently more-and-more data, it is difficult to generate adequate visual representations. The visualization of interesting patterns hidden in such large data sets has the difficulty of requiring a much higher complexity and resolution. Therefore they are also much larger than available visual encodings and screen spaces can handle. The screen space, e.g. the amount of pixels of modern output devices, does not increase in the same manner as the flood of data. Therefore, it is im- portant to find ways to use the limited space optimally. Visualization is essential to surveying and exploring the data. Although geographic and statistical visualization have been studied for many decades, the scale of the data presents new challenges (10, 11). Displaying large point sets on conventional maps is problematic. Over-plotting ob- scures data points in densely populated areas, while sparsely popu- lated areas waste space and supply only insufficient detailed infor- mation. Small clusters are difficult to find - they are not noticeable enough, and are sometimes even occluded by large clusters. In this study, we demonstrate an approach which distorts the large point sets continuously without destroying neighborhoods with a combination of clustering and scaling to meet some of the challenges of large- scale geo-visualization data. Neighborhood preservation means that the topological order of points is kept. Also, the basic ideas of dis- torting dense and sparse areas by using the screen space optimal must be addressed. We introduce an efficient way of distorting by detecting dense and sparse areas of the data distribution and through re-scaling the polar-coordinate locations of the data points. In addition, the new approaches introduce a multi-scaling feature that takes many localities and local features of the data into account. 2 RELATED WORK Visualizing large geo-spatial data sets using pixel-based techniques involves mapping the two geo-spatial dimensions of a data point to screen coordinates and appropriately encoding the associated statistical value by color. The points of the input set are assumed to have one or more associated statistical attributes. Informally, our goal is to show clusters and other relationships between points, determined by both locations and statistical values. By considering just one statistical attribute at a time, we can interpret geo-spatial data sets as points in 3-D: the two geo-spatial dimensions and a third statistical dimension. We note that real-world data set distributions are often highly non-uniform, and data points form readily-identifiable 3-D point clouds. A common approach in visualization is to apply local placement functions that transform the input data set into a solution set and make patterns of interest more obvious. One example to