Privacy-Preserving Recommendations With Mixture Model-Based Matrix Factorization Under Local Differential Privacy

Matrix factorization-based recommendations have emerged as a cornerstone for many industrial recommendation algorithms. However, studies employing differential privacy often rely on a trusted server, while those implementing local differential privacy (LDP) frequently encounter substantial accuracy degradation and excessive communication overhead due to noise injection and frequent user interactions. Moreover, the presence of injected noise for privacy protection and inherent Gaussian noise within these perturbed values compounds the accuracy issues and may create a cascading effect under LDP, exacerbating the complexity of the problem at hand. To address these challenges, we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MENTOR</i>, which is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i>ixture model-based r<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i>comme<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i>dations approach with matrix Fac<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TOR</i>ization under LDP. Its main idea lies in the adoption of a bounded input perturbation mechanism that closely approximates the Laplace distribution while providing rigorous LDP, coupled with accounting for various noise types present in the perturbed data. This approach allows us to reformulate the matrix factorization process with minimal user interaction, requiring only a single round of communication. In particular, to add noise, we design a bidirectional bounded LDP input perturbation mechanism <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BBV</i> while minimizing variance. To generate recommendation results, we devise a matrix factorization technique <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GLMF</i> based on a Gaussian–Laplacian mixture model. Comprehensive experiments reveal that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MENTOR</i> outperforms the state of the art by at least 15% in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RMSE</i> and 12% in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F-Measure</i>, showcasing its effectiveness in balancing privacy and utility in recommendation systems.