Optimized and federated soft-impute for privacy-preserving tensor completion in cyber-physical-social systems

•User-level differentially private protection. The (epsilon, delta)-joint differential privacy of Gaussian mechanism to protect all data of a user against differential attacks.•High efficiency and high accuracy. An optimized federated soft-impute algorithm with differentially private guarantee to achieve tensor completion with respect to better accuracy and higher efficiency.•Theoretical privacy and utility analysis. Formal recovery error bound is provided, and strong utility guarantee and privacy guarantee are proved.