With recent sensor and tracking technology advances, the volume of available trajectory data is steadily increasing. Consequently, managing and analyzing trajectory data has seen significant interest from the research community. The challenges presented by trajectory data arise from their spatio-temporal nature as well as the uncertainty regarding locations between sampled points. In this paper, we present a formal spatio-temporal predicate logic with configurable strictness parameters and two novel operators: (1) a spatio-temporal selection operator for filtering trajectories, and (2) a spatio-temporal crop operator for extracting relevant sub-trajectories based on spatio-temporal predicates. Furthermore, we integrate a similarity-based join operators for flexible trajectory comparison. Finally, we show that our predicate logic is expressive enough to capture all spatial and temporal relations put forward by previous work.

Trajectory clustering is one of the most important data mining tasks on this spatio-temporal data type. Many existing algorithms perform clustering by employing a distance measure designed specifically for trajectory data. However, compared to the clustering of n-dimensional points, the choice of a suitable distance measure for trajectory data is not straightforward. In this work, we conduct an experimental evaluation to examine the efficacy of different trajectory distance measures in relation to different data sets and different clustering algorithms. Our experiments show noticeable trends in the distribution of distance measure performance, dependent on clustering method and data set characteristics.

The availability of GPS sensors in vehicles has enabled the collection of trajectory data that can be utilized to improve the quality of location-based services. However, mostly due to privacy concerns, many data sets are published without containing entire trajectories but only the source location, the target location and the duration of recorded trips. In this paper, we study the problem of route recovery from trip data. In contrast to recent works that assume the availability of entire trajectories for past trips, we investigate methods for route recovery in the absence of such historical data, and we present methods for recovering the single most likely route that a vehicle has travelled. Furthermore, we introduce the region recovery problem that aims at determining a small region that is very likely to contain the traveled route. We also introduce region recovery methods for both single trips and trip groups. In a comprehensive experimental evaluation, we study the efficacy of our solutions for both the route and the region recovery problem. For the region recovery problem in particular, we demonstrate the pros and cons of each method along with the trade-off they offer between the size of the recovered region and the likelihood that the region contains the actual route.