Tri-Space: Conceptualization, Transformation, Visualization

The tri-space is a concept that has been periodically put forth within geographic information science over the last few decades, under various guises and names (Openshaw 1994; Peuquet 1994; Turton et al. 2000; Yuan 1994). It refers to the conjunction of three spaces: geographic space, time space, and attribute space. These three elements are easily identified in typical spatio-temporal data sets. For example, when such data are distributed in tabular form, we will often come across cases where a single row holds the observations for a particular geographic locus at a particular moment in time and a single column refers to all observations for a particular attribute. In other datasets, one might find rows referring to one attribute at one geographic location, while columns hold all values for a particular time slice. Interestingly, such different logical data structures could express absolutely identical source data, though we are looking at different reexpressions of such source data in the form of differently constructed objects existing in a differently constructed high-dimensional spaces. Take for example a data set consisting of observations for seven crime variables in fifty states captured in forty annual slices. Such a data set would thus consist of 14,000 atomic values. The proposal put forth here is that by interpreting such data within a trispace based conceptualization we could derive systematic reexpressions, without requiring any data reduction or aggregation at an early stage of processing.