Matrix completion has important applications in trajectory recovery and mobile social networks. However, sending raw data containing personal, sensitive information to cloud computing nodes may lead to privacy exposure issue.The privacy-preserving matrix completion is a useful approach to perform matrix completion while preserving privacy. In this paper, we propose a high-performance method for privacy-preserving matrix completion. First,we use a lightweight encryption scheme to encrypt the raw data and then perform matrix completion using alternating direction method of multipliers (ADMM). Then,the complemented matrix is decrypted and compared with the original matrix to calculate the error. This method has faster speed with higher accuracy. The results of numerical experiments reveal that the proposed method is faster than other algorithms.

翻译：矩阵补全在轨迹恢复和移动社交网络中具有重要应用。然而，将包含个人敏感信息的原始数据传输至云计算节点可能导致隐私泄露问题。隐私保护矩阵补全是一种在保护隐私的同时实现矩阵补全的有效方法。本文提出了一种高性能的隐私保护矩阵补全方法。首先，采用轻量级加密方案对原始数据进行加密，随后利用交替方向乘子法（ADMM）执行矩阵补全。其次，对补全后的矩阵进行解密，并与原始矩阵比较以计算误差。该方法在实现更高精度的同时具有更快的速度。数值实验结果表明，所提方法相比其他算法具有更快的运行速度。