We propose a novel algorithm to ensure @math -differential privacy for answering range queries on trajectory data. In order to guarantee privacy, differential privacy mechanisms add noise to either data or query, thus introducing errors to queries made and potentially decreasing the utility of information. In contrast to the state-of-the-art, our method achieves significantly lower error as it is the first data- and query-aware approach for such queries. The key challenge for answering range queries on trajectory data privately is to ensure an accurate count. Simply representing a trajectory as a set instead of of points will generally lead to highly inaccurate query answers as it ignores the sequential dependency of location points in trajectories, i.e., will violate the consistency of trajectory data. Furthermore, trajectories are generally unevenly distributed across a city and adding noise uniformly will generally lead to a poor utility. To achieve differential privacy, our algorithm adaptively adds noise to the input data according to the given query set. It first privately partitions the data space into uniform regions and computes the traffic density of each region. The regions and their densities, in addition to the given query set, are then used to estimate the distribution of trajectories over the queried space, which ensures high accuracy for the given query set. We show the accuracy and efficiency of our algorithm using extensive empirical evaluations on real and synthetic data sets.
@cite_20 define the dependency between cells instead of points by mapping the trajectories to a grid to count the movement frequencies between the adjacent cells. However, a frequency vector only maintains the number of transitions for a group of observations without information about the spatial adjacency of two vectors. This information is crucial for a range query as it counts the vectors overlapping the query area. In our work, we use a spatial histogram that is a grid but captures both the cell counts and the spatial adjacency of trajectories.
@cite_20
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Due to the high uptake of location-based services (LBSs), large spatio-temporal datasets of moving objects' trajectories are being created every day. An important task in spatial data analytics is to service range queries by returning trajectory counts within a queried region. The question of how to keep an individual user's data private whilst enabling spatial data analytics by third parties has become an urgent research direction. Indeed, it is increasingly becoming a concern for users. To preserve privacy we discard individual trajectories and aggregate counts over a spatial and temporal partition. However the privacy gained comes at a cost to utility: trajectories passing through multiple cells and re-entering a query region, lead to inaccurate query responses. This is known as the distinct counting problem. We propose the Connection Aware Spatial Euler (CASE) histogram to address this long-standing problem. The CASE histogram maintains the connectivity of a moving object path, but does not require the ID of an object to distinguish multiple entries into an arbitrary query region. Our approach is to process trajectories offline into aggregate counts which are sent to third parties, rather than the original trajectories. We also explore modifications of our aggregate counting approach that preserve differential privacy. Theoretically and experimentally we demonstrate that our method provides a high level of accuracy compared to the best known methods for the distinct counting problem, whilst preserving privacy. We conduct our experiments on both synthetic and real datasets over two competitive Euler histogram-based methods presented in the literature. Our methods enjoy improvements to accuracy from 10 up to 70 depending on trip data and query region size, with the greatest increase seen on the Microsoft T-Drive real dataset, representing a more than tripling of accuracy. Studying trajectories of individuals has received growing interest. The aggregated movement behaviour of people provides important insights about their habits, interests, and lifestyles. Understanding and utilizing trajectory data is a crucial part of many applications such as location based services, urban planning, and traffic monitoring systems. Spatial histograms and spatial range queries are key components in such applications to efficiently store and answer queries on trajectory data. A spatial histogram maintains the sequentiality of location points in a trajectory by a strong sequential dependency among histogram cells. This dependency is an essential property in answering spatial range queries. However, the trajectories of individuals are unique and even aggregating them in spatial histograms cannot completely ensure an individual's privacy. A key technique to ensure privacy for data publishing ϵ-differential privacy as it provides a strong guarantee on an individual's provided data. Our work is the first that guarantees ϵ-differential privacy for spatial histograms on trajectories, while ensuring the sequentiality of trajectory data, i.e., its consistency. Consistency is key for any database and our proposed mechanism, PriSH, synthesizes a spatial histogram and ensures the consistency of published histogram with respect to the strong dependency constraint. In extensive experiments on real and synthetic datasets, we show that (1) PriSH is highly scalable with the dataset size and granularity of the space decomposition, (2) the distribution of aggregate trajectory information in the synthesized histogram accurately preserves the distribution of original histogram, and (3) the output has high accuracy in answering arbitrary spatial range queries. 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. This work addresses the problem of aggregation of trajectories data. Specifically, we propose a tree-based data structure for counting vehicle trajectories by mapping them into a set of spatial histograms with different granularities. We also present an approach for processing spatio-temporal range queries by aggregating the histograms in the query rectangles. The proposed methodology can be used for preserving the privacy of vehicle drivers by maintaining aggregated trajectory data. In addition, as we show, it can be used to handle the well-known distinct counting problem. Experimental results show that the new data structure achieves a high level of accuracy in query results and consistently outperforms the leading histogram-based approach.