Sets or collections of items occur naturally in many settings. We may talk about different types of restaurants, models of cars, unions of countries, and so forth. A data set can have a number of such sets – countries lie on a continent, are possibly part of the EU, NATO, UN, and/or various trade unions, or even grouped by other characteristics such as carbon dioxide emission, gross domestic product, internet usage. If we want to analyze how these groups relate to one another, we’re typically interested in finding intersections (which countries in the EU have a low carbon dioxide emission), unions (which countries either have a high GDP or part of NATO) and differences (which countries in the Europe are not part of the EU.
The above example shows that geography can play a role in analyzing such set systems. However, current state-of-the-art visualization forces a choice: either one discards geography completely to visualize the sets, or one uses a precise map, almost fully dictating the layout of the graphical elements. We are currently working on methods to visualize set systems in a spatially informative way – that is, geography plays a role in its layout, but does not dominate it: we allow distortions of space to further clarify structures and patterns in the set system. The figure below demonstrates an example, where we combine a “small multiples with gaps” layout with a visual representation of colored polygons to indicate the various sets.