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.
Recently, @cite_13 developed a mechanism named Private Spatial Histogram for range queries on trajectories. publishes a synthetic spatial histogram under @math -differential privacy. It is a query-aware mechanism that extends the idea of in @cite_3 . , takes a spatial histogram and a query set as input and utilizes the correlation between the queries to estimate the distribution of the original histogram privately. To maintain the consistency in the histogram, uses a approach that may result in a histogram far from the original spatial histogram. The reason lies in the approach that locally ensures consistency and may lead to overcorrection. In this paper, we propose a data- and query- aware mechanism that utilizes the trajectories density in different regions as well as the given queries correlation to estimate the optimal spatial histogram with significantly higher utility. Our query-aware strategy employs a linear programming approach to provide a guarantee on optimally consistent histogram which leads to significant improvement in the utility of results.
@cite_13 @cite_3
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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. We present a new algorithm for differentially private data release, based on a simple combination of the Multiplicative Weights update rule with the Exponential Mechanism. Our MWEM algorithm achieves what are the best known and nearly optimal theoretical guarantees, while at the same time being simple to implement and experimentally more accurate on actual data sets than existing techniques.