Collaborative filtering (CF) recommendation is well-known for its outstanding recommendation performance, but previous researches showed that it could cause privacy leakage for users due to $k$-nearest neighboring (KNN) attacks. Recently, the notion of differential privacy (DP) has been applied to privacy preservation in recommendation systems. However, as far as we know, existing differentially private CF recommendation systems degrade the recommendation performance (such as recall and precision) to an unacceptable level. In this paper, to address the performance degradation problem, we propose a differentially private user-based CF recommendation system based on $k$-means clustering (KDPCF). Specifically, to improve the recommendation performance, KDPCF first clusters the dataset into categories by $k$-means clustering and appropriately adjusts the size of the target category to which the target user belongs, so that only users in the well-sized target category are used for recommendation. Then, it selects efficiently a set of neighbors from the target category at one time by employing only one instance of exponential mechanism instead of the composition of multiple ones, and then uses a CF algorithm to recommend based on this set of neighbors. We theoretically prove that our system achieves differential privacy. Empirically, we use two public datasets to evaluate our recommendation system. The experimental results demonstrate that our system has a significant performance improvement compared to existing ones.

协作过滤（CF）推荐以其出色的推荐性能而闻名，但以前的研究表明，它可能会由于以下原因而导致用户隐私泄露： $ķ$-最近邻（KNN）攻击。最近，差分隐私（DP）的概念已应用于推荐系统中的隐私保护。但是，据我们所知，现有的差分专用CF推荐系统将推荐性能（如召回率和准确性）降到了不可接受的水平。在本文中，为了解决性能下降的问题，我们提出了一种基于差分私有用户的基于CF的推荐系统$ķ$-均值群集（KDPCF）。具体来说，为了提高推荐效果，KDPCF首先通过以下方式将数据集聚为类别：$ķ$-表示聚类，并适当调整目标用户所属的目标类别的大小，以便仅将大小合适的目标类别中的用户用于推荐。然后，它仅通过采用指数机制的一个实例而不是多个实例的组合，一次有效地从目标类别中选择一组邻居，然后使用CF算法基于该组邻居进行推荐。我们从理论上证明了我们的系统实现了差异隐私。根据经验，我们使用两个公共数据集来评估我们的推荐系统。实验结果表明，与现有系统相比，我们的系统具有显着的性能改进。