An improved matrix factorization with local differential privacy based on piecewise mechanism for recommendation systems

Matrix factorization (MF) is a prevailing technique in recommendation systems (RSs). Since MF needs to process a large amount of user data when generating recommendation results, privacy protection is increasingly being valued by users. Many existing privacy-preserving MF schemes only protect users' rating values, but ignore the privacy preservation of item sets rated by users. To make up for this shortcoming, a strategy based on piecewise mechanism (PM) is specially designed to simultaneously protect the privacy of rating values and item sets rated by users. To utilize data effectively, an improved MF based on PM (IMFPM) is proposed by dividing item profiles into global and personal information. Furthermore, in the IMFPM, random projection technology is used to reduce the influence of privacy noise on the estimation error. Theoretical analysis and experiment results show that the IMFPM not only provides strong differential privacy protection for rating values and item sets rated by users, but also has high prediction quality. Thus, the IMFPM is a good candidate scheme with privacy preservation for distributed recommendation systems.