A mutual correlation between trajectories of two users is very helpful to real-life applications such as product recommendation and social media. While providing tremendous benefits, the releasing of correlated trajectories may leak sensitive social relations, due to potential links between mutual correlations and social relations. To the best of our knowledge, we take the first step to propose a mathematically rigorous $n$n-body Laplace framework, satisfying $\varepsilon$ɛ-differential privacy, which efficiently prevents a social relation inference through the mutual correlation between $n$n-node trajectories of two users. The problem is mathematically formulated by defining a trajectory correlation score to measure the social relation between two users. Then, under the $n$n-body Laplace framework, we propose two Lagrange Multiplier-based Differentially Private (LMDP) approaches to optimize the privacy budgets, for the data utility measured by location distances and the data utility measured by location correlations, i.e., UD-LMDP and UC-LMDP. Also, we present detailed analyses of privacy, data utility, adversary knowledge and the constrained optimizations. Finally, we perform experimental studies with real-life data. Our experimental results show that our proposed approaches achieve better privacy and data utility than the existing approaches.

中文翻译：

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释放相关轨迹：走向高效用和最优差分隐私

两个用户的轨迹之间的相互关联对于产品推荐和社交媒体等现实生活中的应用非常有帮助。在提供巨大好处的同时，由于相互关联和社会关系之间的潜在联系，相关轨迹的释放可能会泄漏敏感的社会关系。据我们所知，我们迈出了第一步，提出了一个数学上严格的$n$n-body 拉普拉斯框架，满足 $\varepsilon$ɛ- 差分隐私，通过相互之间的相互关联有效地防止社会关系推断 $n$n- 两个用户的节点轨迹。通过定义轨迹相关性分数来衡量两个用户之间的社会关系，该问题在数学上被公式化。然后，根据$n$n-body Laplace 框架，我们提出了两种基于拉格朗日乘数的差分隐私 (LMDP) 方法来优化隐私预算，用于通过位置距离测量的数据效用和通过位置相关性测量的数据效用，即 UD-LMDP 和 UC-LMDP . 此外，我们还详细分析了隐私、数据效用、对手知识和约束优化。最后，我们使用真实数据进行实验研究。我们的实验结果表明，我们提出的方法比现有方法实现了更好的隐私和数据效用。