Joining trajectory datasets is a significant operation in mobility data analytics and the cornerstone of various methods that aim to extract knowledge out of them. In the era of Big Data, the production of mobility data has become massive and, consequently, performing such an operation in a centralized way is not feasible. In this paper, we address the problem of Distributed Subtrajectory Join processing by utilizing the MapReduce programming model. Compared to traditional trajectory join queries, this problem is even more challenging since the goal is to retrieve all the "maximal" portions of trajectories that are "similar". We propose three solutions: (i) a well-designed basic solution, coined DTJb, (ii) a solution that uses a preprocessing step that repartitions the data, labeled DTJr, and (iii) a solution that, additionally, employs an indexing scheme, named DTJi. In our experimental study, we utilize a 56GB dataset of real trajectories from the maritime domain, which, to the best of our knowledge, is the largest real dataset used for experimentation in the literature of trajectory data management. The results show that DTJi performs up to 16x faster compared with DTJb, 10x faster than DTJr and 3x faster than the closest related state of the art algorithm.
A similar but different problem is the one of trajectory similarity join, where the goal is to retrieve all pairs of trajectories that exceed a given similarity threshold as in @cite_32 and @cite_20 . However, both of them return as a result pairs of trajectories and not subtrajectories, thus they cannot support some of the scenarios presented in . An approach very similar to ours is presented in @cite_23 , where, given a pair of trajectories they try to perform partial matching, finding the most similar subtrajectories between these two trajectories. Different variations of the problem are presented, where the duration of the match'' is specified beforehand or not. Nevertheless, the problem in @cite_23 is not a join operation and temporal tolerance is not considered. To sum up, all of the above approaches are centralized and applying them to a parallel and distributed environment is non-trivial.
@cite_23 @cite_32 @cite_20
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The matching of similar pairs of objects, called similarity join, is fundamental functionality in data management. We consider the case of trajectory similarity join (TS-Join), where the objects are trajectories of vehicles moving in road networks. Thus, given two sets of trajectories and a threshold θ, the TS-Join returns all pairs of trajectories from the two sets with similarity above θ. This join targets applications such as trajectory near-duplicate detection, data cleaning, ridesharing recommendation, and traffic congestion prediction. With these applications in mind, we provide a purposeful definition of similarity. To enable efficient TS-Join processing on large sets of trajectories, we develop search space pruning techniques and take into account the parallel processing capabilities of modern processors. Specifically, we present a two-phase divide-and-conquer algorithm. For each trajectory, the algorithm first finds similar trajectories. Then it merges the results to achieve a final result. The algorithm exploits an upper bound on the spatiotemporal similarity and a heuristic scheduling strategy for search space pruning. The algorithm's per-trajectory searches are independent of each other and can be performed in parallel, and the merging has constant cost. An empirical study with real data offers insight in the performance of the algorithm and demonstrates that is capable of outperforming a well-designed baseline algorithm by an order of magnitude. Emerging vehicular trajectory data have opened up opportunities to benefit many real-world applications, e.g., frequent trajectory based navigation systems, road planning, car pooling, etc. The similarity join is a key operation to enable such applications, which finds similar trajectory pairs from two large collections of trajectories. Existing similarity metrics on trajectories rely on aligning sampling points of two trajectories. However, due to different sampling rates or different vehicular speeds, the sample points in similar trajectories may not be aligned. To address this problem, we propose a new bi-directional mapping similarity ( @math ), which allows a sample point of a trajectory to align to the closest location (which may not be a sample point) on the other trajectory, and vice versa. Since it is expensive to enumerate every two trajectories and compute their similarity, we propose Strain-Join , a signature-based trajectory similarity join framework. Strain-Join first generates signatures for each trajectory such that if two trajectories do not share common signatures, they cannot be similar. In order to utilize this property to prune dissimilar pairs, we devise several techniques to generate high-quality signatures and propose an efficient filtering algorithm to prune dissimilar pairs. For the pairs not pruned by the filtering algorithm, we propose effective verification algorithms to verify whether they are similar. Experimental results on real datasets show that our algorithm outperforms state-of-the-art techniques in terms of both effectiveness and efficiency. We address the problem of performing efficient similarity join for large sets of moving objects trajectories. Unlike previous approaches which use a dedicated index in a transformed space, our premise is that in many applications of location-based services, the trajectories are already indexed in their native space, in order to facilitate the processing of common spatio-temporal queries, e.g., range, nearest neighbor etc. We introduce a novel distance measure adapted from the classic Frechet distance, which can be naturally extended to support lower upper bounding using the underlying indices of moving object databases in the native space. This, in turn, enables efficient implementation of various trajectory similarity joins. We report on extensive experiments demonstrating that our methodology provides performance speed-up of trajectory similarity join by more than 50 on average, while maintaining effectiveness comparable to the well-known approaches for identifying trajectory similarity based on time-series analysis. Spatio-temporal and geo-referenced datasets are growing rapidly, with the rapid development of some technology, such as GPS, satellite systems. At present, many scholars are very interested in the clustering of the trajectory. Existing trajectory clustering algorithms group similar trajectories as a whole and can't distinguish the direction of trajectory. Our key finding is that clustering trajectories as a whole could miss common sub-trajectories and trajectory has direction information. In many applications, discovering common sub-trajectories is very useful. In this paper, we present a trajectory clustering algorithm CTHD (clustering of trajectory based on hausdorff distance). In the CTHD, the trajectory is firstly described by a sequence of flow vectors and partitioned into a set of sub-trajectory. Next the similarity between trajectories is measured by their respective Hausdorff distances. Finally, the trajectories are clustered by the DBSCAN clustering algorithm. The proposed algorithm is different from other schemes using Hausdorff distance that the flow vectors include the position and direction. So it can distinguish the trajectories in different directions. The experimental result shows the phenomenon.