Higher order information includes k-nearest neighbor information and k-order region information that are of great importance when the first order or lower order information is not functioning. Despite of the importance of direction in spatio-temporal analysis, directional higher order information has received almost no attention. This paper introduces a new directional higher order information dissimilarity measure that combines topological and geometrical information for spatio-temporal trajectories. It also presents a spider chart-like visualisation approach for directional higher order information and demonstrates the usefulness of this measure with a case study from top-k trajectory mining.Keywords-Higher order information; spatio-temporal trajectory; higher order Voronoi diagrams; directional information;
I. INTRODUCTIONHigher Order Information (HOI) includes k-nearest neighbor information and k-order region information that are of great importance when the first order or lower order information is not functioning properly. Uncertainty in modern society requires "what-if" analysis to explore different scenarios for better decision making. HOI provides necessary information for "what-if" analysis, and it has been researched for many years with various applications in GIS and emergency management [1].Based on the spatio-temporal characteristics of HOI, HOI can be classified into three different types: namely geometrical HOI, topological HOI and directional HOI. Directional HOI is about relative positioning properties with distance information. Despite the importance of direction in spatio-temporal analysis, directional HOI has attracted no attention even though some studies investigated and applied geometrical HOI [2], [3], [4] and topological HOI [5]. Trajectory is a typical example of spatio-temporal data capable of representing object dynamics. Trajectory of moving objects such as cars, humans, birds, or other objects is useful in decision making processes in many application domains such as animal movement [6], sport team strategies [7], surveillance analysis [8], [9], transport analysis [10], [11], emergency management [1], and supermarket shopping paths [12]. Improvement in tracking and sensing technologies facilitates a collection of vast volume of usergenerated trajectory data at very low cost. Researchers have