Putting Data on the Map

Summary

Visualization allows us to perceive relationships in large sets of interconnected data. While statistical techniques may determine correlations among the data, visualization helps us frame what questions to ask about the data. The design and implementation of algorithms for modeling, visualizing and interacting with large relational data is an active research area in data mining, information visualization, human-computer interaction, and graph drawing.

Map representations provide a way to visualize relational data with the help of conceptual maps as a data representation metaphor. In a narrow sense, a map representation of a graph is a contact graph representation where the adjacency of vertices is expressed by regions that share borders. Such representations are, however, limited to planar graphs by definition. We can extend the notion of a map representation to non-planar graphs by generalizing the idea as follows: clusters of well-connected vertices form countries, and countries share borders when neighboring clusters are tightly interconnected.

Information spatialization and cartograms also connect the notions of data with those of maps. Cartograms redraw an existing geographic map such that the country areas are proportional to some metric (e.g., population), an idea that dates back to a paper by Raisz in 1934 and is still popular today. Spatialization is the process of assigning two- or three-dimensional coordinates to abstract data points, ideally such that the spatial mapping has much of the characteristics of the original high-dimensional space. Multi-dimensional scaling or principal component analysis are techniques that allow us to spatialize high-dimensional data. Techniques like information landscapes can then be used to convert the resulting two-dimensional coordinates into meaningful three-dimensional landscapes.

Providing efficient and effective data visualization is a difficult challenge in many real-world software systems. One challenge lies in developing algorithmically efficient methods to visualize large and complex data sets. Another challenge is to develop effective visualizations that make the underlying patterns and trends easy to see. And finally, we need to allow users to interactively access, analyze, and filter these patterns in an intuitive manner. All of these tasks are becoming increasingly more difficult due to the growth of the data sets arising in modern applications, as well as due to their highly dynamic nature.