一种基于差分隐私的矩阵填充算法
A Matrix Completion Algorithm Based on Differential Privacy
摘要: 矩阵填充作为矩阵分析中的一个关键课题，对于处理不完整数据集至关重要，其应用广泛，覆盖图像处理、推荐系统等领域。与此同时，隐私保护在数据安全领域占据核心地位，旨在确保个人敏感信息在数据分析过程中得到充分的安全保障和保密处理。将这两个领域的研究结合，为应对实际应用中的复杂挑战提供了创新性的解决方案。文章提出了一种基于差分隐私的新型隐私保护矩阵填充方案。该方案巧妙地融合了差分隐私理论框架，通过向原始数据中添加噪声来保护用户隐私。这种做法确保了即使在数据公开或共享的情况下，个体的信息也不会被泄露，从而有效地防止了潜在的隐私风险。数值实验结果表明，所提出的方案不仅能够显著保护用户的隐私，同时还在保持数据效用方面表现出色。此外，该方法还提升了算法运行效率，降低了计算成本。
Abstract: Matrix completion, as a key topic in matrix analysis, is crucial for dealing with incomplete datasets, and its applications cover a wide range of fields, such as image processing and recommender systems. Meanwhile, privacy protection occupies a central position in the field of data security, aiming to ensure that personal sensitive information is adequately secured and confidentially handled during data analysis. Combining research in these two fields provides innovative solutions to address the complex challenges in practical applications. In this paper, we propose a novel privacy-preserving matrix completion scheme based on differential privacy. The scheme cleverly incorporates a differential privacy theoretical framework to protect user privacy by adding noise to the raw data. This approach ensures that individuals’ information is not disclosed even when the data is public or shared, thus effectively preventing potential privacy risks. Numerical experimental results show that the proposed scheme not only significantly protects user privacy, but also excels in maintaining data utility. In addition, the method improves the algorithm operation efficiency and reduces the computational cost.
文章引用：郭佳浩. 一种基于差分隐私的矩阵填充算法[J]. 应用数学进展, 2025, 14(2): 162-170. https://doi.org/10.12677/aam.2025.142061

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