Data synthesis under Local Differential Privacy (LDP) presents a promising approach for private data analysis and sharing, as it enables the execution of all analysis tasks on raw data without the need for a trusted aggregator. The select-measure-generate paradigm of data synthesis under Differential Privacy (DP) introduces specific challenges in the context of LDP, particularly because the noise inherent to LDP is significantly greater than that of DP, especially in high-dimensional datasets. The “select” step involves calculating the correlations between attributes to identify important marginal measurements (attribute pairs), while the “measure” step aims to estimate the frequency distribution of each selected marginal under LDP. However, the utility of both the correlation and frequency estimation for multidimensional data is often unsatisfactory under LDP, as the utility of data analysis tasks typically declines with an increasing number of dimensions. To address these issues, we propose a two-stage method, named FilterLDPSyn. In Stage 1, it filters out ineffective measurements based on one-dimensional frequency and entropy estimations under LDP. In Stage 2, it enhances the utility of the distribution by iteratively collecting two-dimensional values and restoring consistency between one- and two-dimensional distributions. Experimental results demonstrate the superiority of our proposed method over existing approaches.

With the widespread use of smart phones and mobile Internet, social network users have generated massive geo-tagged tweets, photos and videos to form lots of informative trajectories which reveal not only their spatio-temporal dynamics, but also their activities in the physical world. Existing spatial trajectory query studies mainly focus on analyzing the spatio-temporal properties of the users’ trajectories, while leaving the understanding of their activities largely untouched. In this paper, we incorporate the semantics of the activity information embedded in trajectories into query modelling and processing, with the aim of providing end users more informative and meaningful results. To this end, we propose a novel trajectory query that not only considers the spatio-temporal closeness but also, more importantly, leverages a proven technique in text mining field, probabilistic topic modelling, to capture the semantic relatedness of the activities between the data and query. To support efficient query processing, we design a hierarchical grid-based index by integrating the probabilistic topic distribution on the substructures of trajectories and their spatio-temporal extent at the corresponding level of the index hierarchy. This specialized structure enables a top-down search algorithm to traverse the index while pruning unqualified trajectories in spatial and topical dimensions simultaneously. The experimental results on real-world datasets demonstrate the good efficiency and scalability performance of the proposed indices and trajectory search methods.