4D Time Density of Trajectories: Discovering Spatiotemporal Patterns in Movement Data

Yebin Zou, Yijin Chen, Jing He, Gehu Pang, Kaixuan Zhang
2018 ISPRS International Journal of Geo-Information  
Modern positioning and sensor technology enable the acquisition of movement positions and attributes on an unprecedented scale. Therefore, a large amount of trajectory data can be used to analyze various movement phenomena. In cartography, a common way to visualize and explore trajectory data is to use the 3D cube (e.g., space-time cube), where trajectories are presented as a tilted 3D polyline. As larger movement datasets become available, this type of display can easily become confusing and
more » ... legible. In addition, movement datasets are often unprecedentedly massive, high-dimensional, and complex (e.g., implicit spatial and temporal relations and interactions), making it challenging to explore and analyze the spatiotemporal movement patterns in space. In this paper, we propose 4D time density as a visualization method for identifying and analyzing spatiotemporal movement patterns in large trajectory datasets. The movement range of the objects is regarded as a 3D geographical space, into which the fourth dimension, 4D time density, is incorporated. The 4D time density is derived by modeling the movement path and velocity separately. We present a time density algorithm, and demonstrate it on the simulated trajectory and a real dataset representing the movement data of aircrafts in the Hong Kong International and the Macau International Airports. Finally, we consider wider applications and further developments of time density. area within which animals usually confine their normal activities (foraging, mating and taking care of young) [7] . Another concept associated with the home range is the utilization distribution [8], which is a probability surface on the 2D region that represents the possibility of finding animals in a particular area [1, 9, 10] . The home range is usually defined by the probabilistic contour of a certain value of the utilization distribution surface. It usually uses a 0.95 probability, but the choice is subjective and can vary depending on the study [1] . However, these two concepts often focus on the spatial distribution of the measured positions only in 2D space and ignore the time series of the measurements. One notion that has persisted in wildlife ecology is the space usage patterns of animals' movement. Animals prefer to spend more time at particular locations, or visit a given place frequently, or move slowly/quickly in some areas, making their living environment uneven [11] [12] [13] . Ecologists are particularly interested in exploring the role of time in this heterogeneous behavior [1, 14] . However, most of the methods for home range/utilization distribution estimation [15] [16] [17] [18] [19] are only associated with two spatial dimensions, and seldom consider the time dimension; this makes it difficult to visually discover the spatiotemporal patterns of movement. Thus, another potential development we can see is to extend the calculation of home range/utilization distribution into a real 3D geographical space (i.e., using elevation as the third dimension). This is of great significance to animals moving in the air or in water, and animals often changing their vertical distribution relative to external environmental factors [1, 20, 21] . We expect that the movement range of birds or marine creatures can be viewed as a 3D geographic space [1, 22] , and time, specifically the function of time (3D analogy of utilization distribution), would now represent the fourth dimension. A 3D space, with three spatial axes, forms a three-dimensional geographic space, and is used to visualize the spatial aggregation of the collected movement trajectories. This is where the data cube is incorporated into the trajectory data visualization. We propose 4D time density as an effective method for analyzing and identifying spatiotemporal movement patterns in large trajectory datasets. This approach was inspired by the space-time density of trajectories [1,2] and the home range/utilization distribution concept in wildlife ecology [10, 17] . However, we changed the algorithm for density calculation, incorporating the fourth dimension-4D time density into 3D geographic space, instead of the 2D geographic space. The 4D time density is derived by dividing the normalized path length by aggregated velocity. In addition, time density and utilization distribution are conceptually slightly different. Time density is a measure of the frequency and intensity of a space use of a species, which is associated with the concept of utilization distribution, since the space use intensity is large for places with a large probability of finding a given species. We subsequently describe the trajectory division and cube cell construction methods to establish the computational range of time density, where the traveled distance and aggregated velocity are calculated. The method yields results of space use intensity that are highly correlated with the true probabilities of occurrence (i.e., utilization distribution), and successfully depicts temporal variations in density of occurrence [22] . In a real application case, we present an application of the 4D time density of trajectories on a real dataset that represents the movement data of the aircrafts at the Hong Kong International and the Macau International Airports. The results show that the proposed approach produces density volumes that successfully capture temporal variations in the density of occurrence, and visually identify the specific spatiotemporal patterns of the movement of aircrafts.
doi:10.3390/ijgi7060212 fatcat:edk4hkbdnrfhjbnbpbhun5coqu