一种基于差分隐私的张量填充算法

A Tensor Completion Algorithm Based on Differential Privacy

摘要: 针对高维张量数据填充过程中存在的隐私泄露问题，本文提出一种融合拉普拉斯机制的差分隐私张量填充算法(DP-ADMM-t-SVD)。该算法以ADMM-t-SVD低秩张量填充算法为基础，引入了ε-差分隐私框架，先对观测张量进行逐切片归一化以统一全局敏感度，再对张量在观测位置注入与隐私预算ε相关的拉普拉斯噪声，通过交替方向乘子法迭代求解带隐私约束的张量填充优化问题，实现数据隐私保护与填充精度的双重兼顾。为验证算法可行性，分别在不同尺寸的人工低秩张量数据集和篮球视频现实张量数据集上开展实验，实验结果表明，所提算法在人工和现实数据集上均表现出良好性能：隐私预算ε较小时，算法具备优异的隐私保护效果且恢复精度处于可控范围；ε较大时，恢复精度接近无扰动的基线算法，同时用户可通过调节ε的取值适配不同的隐私保护与恢复精度需求。

Abstract: To address the privacy leakage issue in the completion of high-dimensional tensor data, this paper proposes a differential privacy-preserving tensor completion algorithm integrated with the Laplacian mechanism, denoted as DP-ADMM-t-SVD. Based on the ADMM-t-SVD low-rank tensor completion algorithm, the proposed algorithm introduces the ε-differential privacy framework. It first performs per-slice normalization on the observed tensor to unify the global sensitivity, and then injects Laplacian noise associated with the privacy budget ε only at the observed positions of the tensor. Furthermore, it iteratively solves the privacy-constrained tensor completion optimization problem via the Alternating Direction Method of Multipliers (ADMM), thus realizing a balanced trade-off between data privacy protection and completion accuracy. To verify the feasibility of the proposed algorithm, experiments are carried out on synthetic low-rank tensor datasets with different dimensions and a real-world tensor dataset from a basketball video. Experimental results show that the proposed algorithm achieves favorable performance on both synthetic and real-world datasets: when the privacy budget ε is small, the algorithm provides an excellent privacy protection effect while keeping the completion accuracy within a controllable range; when ε is large, the completion accuracy is close to that of the non-perturbed baseline algorithm. Meanwhile, users can adjust the value of ε to adapt to different requirements for privacy protection and completion accuracy.