High-Performance Privacy-Preserving Matrix Completion for Trajectory Recovery
Jiahao Guo, An-Bao Xu
TL;DR
This work addresses privacy concerns in matrix completion for trajectory recovery by integrating a light-weight encryption scheme with an ADMM-based completion framework. It introduces PPLNM-QR, a CSVD-QR-based, $L_{2,1}$-norm minimisation method that completes encrypted data on cloud nodes and decrypts results on user devices, thereby protecting privacy while preserving accuracy. The framework relies on a tri-factorization $\tilde{M}=\tilde{L}\tilde{D}\tilde{R}$ and an ADMM-driven contraction step to solve a convex $L_{2,1}$ objective with complexity $O(r^2(S+T))$, significantly faster than traditional SVD-based ALT-MIN methods. Experimental results on synthetic and real datasets (including trajectory-related Geolife data) show substantial speedups and low recovery error, demonstrating practical viability for privacy-preserving trajectory recovery and potential applicability to other data-recovery tasks.
Abstract
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.