Similarity Measures for Network Time Prisms

Abstract

GIScience 2016 Short Paper Proceedings Similarity Measures for Network Time Prisms Young Jaegal, Harvey J. Miller Department of Geography, The Ohio State University, 1036 Derby Hall, 154 North Oval Mall, Columbus, OH 43210, U.S.A Email: {jaegal.1; miller.81}@osu.edu Abstract Space-time paths and prisms are time geographic concepts delimiting the actual and potential mobility pattern of an object in space and time, respectively. While there is a range of similarity measures for space-time paths, it is only recently that researchers started to develop similarity measures for the space-time prism (STP). This paper proposes a new methodology for measuring the similarity between network time prisms (NTP), the extension of STP to a moving object on a transportation network. A temporal sweeping method reduces the dimensionality of NTPs to a temporal profile curve that summarizes properties of the NTP subnetwork at moments in time. Then, the existing path similarity measures can measure resemblance between the temporal curves for NTP. We demonstrate the method using selected network summary measures derived from graph theory. 1. Introduction Time geography provides a powerful spatiotemporal framework for both observed and potential movement pattern of moving objects (Hagerstrand, 1970). For observed movement data, space-time paths capture the actual traces of an object in space with respect to time. For the potential mobility, space-time prisms (STPs) delimit the geographic limit of movement of an object with respect to time. Researchers have developed a variety of path similarity measures for quantifying the resemblance between two space-time paths (Long and Nelson, 2013; Ranacher and Tzavella, 2014; Yuan and Raubal, 2014). Previous studies have utilized these measures for various purposes including comparing, clustering and aggregating movement trajectories. However, it is only recently that researchers started paying attention to similarity measures for the STP. Miller, Raubal and Jaegal (2016) develop a temporal sweep approach for measuring STP similarity. The basic idea is to measure selected properties of a STP at moments in time, reducing the dimensionality of a STP to a profile curve summarizing changes in the selected property over time. This paper extends the temporal sweep method for measuring STP similarity to the case of network time prisms (NTPs). We also provide a demonstration of the method using an empirical transportation network. 2. Background 2.1 Network time prism The NTP is an extension of STP that models the potential mobility of an object moving within a transportation network. Since individual movement in the real world usually occurs within networks, the NTP can provide a more realistic model of accessibility than a planar STP. Analytically, the NTP between locations and times (� � , � � , � � ) and (� � , � � , � � ) is the collection of 3-tuples consists of space-time coordinates, (x, y, t), that satisfies the following three conditions (Kuijpers and Othman, 2009).