Tri-Space Modeling and Visualization: Concept, Implementation, and a Case Study in Wildfire Recovery

Multivariate and multitemporal data are bountiful in contemporary society.Examples include hyperspectral land cover monitoring, longitudinal medical studies, climate modeling, and multi-year crime statistics.Geographic information scientists have put forth a number of principal approaches to formally represent such data with a view towards pattern discovery and decision support.These have included the "triad" (Peuquet 1994), "pyramid" (Mennis et al. 2000), and "three-domain" (Yuan 1999) frameworks.Meanwhile, the "tri-space" approach (Skupin 2010, Kolovos et al. 2010, Wang et al. 2013) represents an effort at systematic reconfiguration of multivariate observations for discrete entities at multiple time slices.In the tri-space, an individual observation exists at the intersection of three arrays, typically corresponding to these three elements: locus, time, attribute.Unlike in other frameworks, a locus does not necessarily correspond to a geographic location or object, but merely denotes an entity that has a distinct and persistent identity in some physical or abstract space.The tri-space then proceeds to define objects whose identity is delineated by a particular combination of one or two of these arrays, with the remaining arrays defining an object's location in a particular high-dimensional space.In this manner, six different perspectives can be constructed, to which common multivariate analysis and visualization techniques can then be applied.