Conventional matrix factorization relies on centralized collection of users' data for recommendation, which might introduce an increased risk of privacy leakage especially when the recommender is untrusted. Existing differentially private matrix factorization methods either assume the recommender is trusted, or can only provide a uniform level of privacy protection for all users and items with untrusted recommender. In this paper, we propose a novel Heterogeneous Differentially Private Matrix Factorization algorithm (denoted as HDPMF) for untrusted recommender. To the best of our knowledge, we are the first to achieve heterogeneous differential privacy for decentralized matrix factorization in untrusted recommender scenario. Specifically, our framework uses modified stretching mechanism with an innovative rescaling scheme to achieve better trade off between privacy and accuracy. Meanwhile, by allocating privacy budget properly, we can capture homogeneous privacy preference within a user/item but heterogeneous privacy preference across different users/items. Theoretical analysis confirms that HDPMF renders rigorous privacy guarantee, and exhaustive experiments demonstrate its superiority especially in strong privacy guarantee, high dimension model and sparse dataset scenario.

翻译：传统的矩阵分解依赖集中收集用户数据进行推荐，当推荐系统不可信时，可能会增加隐私泄露风险。现有的差分隐私矩阵分解方法要么假设推荐系统可信，要么在不可信推荐系统场景下仅能为所有用户和物品提供统一的隐私保护水平。本文提出了一种适用于不可信推荐系统的新型异构差分隐私矩阵分解算法（记为HDPMF）。据我们所知，我们首次在不可信推荐系统场景下实现了分布式矩阵分解的异构差分隐私保护。具体而言，我们的框架采用改进的拉伸机制与创新的重缩放方案，实现了隐私保护与精度之间更优的权衡。同时，通过合理分配隐私预算，我们能够在同一用户/物品内部捕获同质隐私偏好，而在不同用户/物品之间捕获异质隐私偏好。理论分析证实HDPMF提供了严格的隐私保证，而大量实验证明了其优越性，尤其是在强隐私保护、高维模型和稀疏数据集场景下。