Space-Time Topological Graphs

Abstract

GIScience 2016 Short Paper Proceedings Space-Time Topological Graphs C. Robertson 1 Wilfrid Laurier University, 75 University Ave, Waterloo, ON Email: crobertson@wlu.ca Abstract The integration of space and time in geospatial analyses is an active research area. While methods for characterizing sequences of spatial point objects over time have evolved greatly over recent years, the treatment of space-time change in complex geographic objects such as linear features and polygons has seen much less attention. In this paper we consider the directed graph as a representation for temporal change in spatial objects, where edges are formed by spatial relationships. With this representation, the large foundation of graph- theoretic metrics and algorithms can be used for the analysis of space-time change in geographic objects. We present preliminary findings using several exemplar datasets: range expansion of polygons representing animal home ranges, the spatial path of Hurricane Katrina, and a forest insect outbreak. In particular, we investigate the dynamics of space-time change in these datasets using well-known metrics for characterizing graph structures. 1. Introduction Understanding space-time change continues to be a challenging and increasingly required task for geospatial analysis, as more spatial datasets are evolving into long-term records of spatial and temporal change (e.g, satellite archives, long-term radio collar studies). However, models of space-time change remain to be fulll developed. Stell et al. (2011) introduced a bigraph representation of space-time change, whereby objects were represented as nodes at discrete time points, and linked through relations. As well, Del Mondo et al. 2012 further developed this model with an explicit spatiotemporal graph representation, distinguishing between filial relations (based on explicit identity) and purely topological relations (derived from spatial relationships). We build on these ideas from the perspective of space-time analysis in order to analyze spatial changes in polygon objects over time. We use several space-time polygon datasets in order to explore a how space-time topological graphs can be used as a representation for spatial-temporal analysis generally. 1.1 Polygon models of space-time change Sadahiro and Umemura (2001) introduced a framework for the analysis of spatio-temporal polygon distributions based on events derived from spatial overlap relations in neighbouring time-steps. The scope of events was extended in Robertson et al. (2007) to include proximity- based spatial relations, describing various types of movement occurring over the change interval, known as spatial-temporal analysis of moving polygons (STAMP). The STAMP framework is temporally discrete, such that an appropriate temporal grain is required a priori in order to represent change. Metrics associated with space-time change include counts of event types, area change, directional change, all of which can be accumulated along paths of the graph representing continuous spatial relationships over time. In Sadahiro (2001) the graph representation of polygon change events was introduced. In this paper we build on this framework order to integrate existing graph metrics into the spatial-temporal analysis of polygon distributions.