LDP-PPA: Local differential privacy protection for principal component analysis

Abstract

Principal component analysis is a fundamental data analysis task, widely used in various fields of data mining. However, it faces several security threats that pose a potential threat to user privacy. Local differential privacy safeguards individual data while permitting the analysis of global user statistics. In this paper, we propose a local differential privacy-preserving principal component analysis method, named LDP-PPA. LDP-PPA provides local differential privacy protection for computing attribute means and user covariance matrices in principal component analysis but suffers serious challenges. For the attribute mean computation, due to the heterogeneity between different attributes, adding the same level of differential privacy noise to different attributes results in different levels of impact. To address this challenge, LDP-PPA maps heterogeneous attribute data to homogeneous data space and perturbs the mapped data in that space through the truncated Laplace mechanism. For user covariance matrix computation, local differential privacy noise can destroy the correlation among data, significantly impacting the accuracy of covariance matrix computations. To address this challenge, LDP-PPA divides the attribute perturbation intervals into high-functionality and low-functionality categories, maintaining the correlation among perturbed data by boosting the likelihood that perturbation outcomes fall within the high-functionality intervals. In addition, we theoretically analyze the privacy of LDP-PPA. Finally, we conducted experimental comparisons of LDP-PPA against existing methods using three publicly available datasets. The results demonstrate that LDP-PPA significantly outperforms current methods in both accuracy and the trade-off between privacy and utility.