Using graphical information from a grid file's directory to visualize patterns in Cartesian product spaces

Data management and data visualization — each an extensively explored field — are rarely considered in conjunction with each other. This is not surprising as they apparently lack a common ground. By example of a region directory, a particular directory for the grid file, we show how an elementary measure, namely data density, can usefully serve data management and data visualization by providing the basis for a common structure. The region directory is a data structure that can — at no extra cost — provide graphical information useful to visualize structures in multivariate data sets with approximate reproductions of the data's variably dense regions. If the centers of these regions are visualized with parallel coordinates, regions with higher or lower than average density (clusters and voids) can be approximately localized. Graphical information for these visualizations is readily available in the region directory, giving the grid file the potential for rapid abstractions from large amounts of data. It is especially noteworthy that the data themselves are not accessed for these displays.