In this big data era, distributed machine learning and global data pooling have become quite critical in practical implementation of any multimedia data-science technique. The emerging federated multimedia recommendation systems (FeMRSs) offer a promising approach to address the need of personalized recommendations subject to both users’ privacy and data security. However, there exists no quantitative method for assessing the discrepancy between the large original rating matrix stored on the server and the dimensionality-reduced rating matrix produced on each client’s equipment. Meanwhile, there lacks a systematic means to evaluate the differential privacy (DP), which is a critical security measure in many distributed systems, particularly when sensitive data are processed. In this work, we first introduce a novel personalized dimensionalityreduction algorithm utilizing the matrix sketching technique. This new algorithm effectively control the difference between the original rating matrix on the server and the dimensionality-reduced rating matrix on each client’s equipment. Moreover, a randomized DP matrix factorization algorithm is designed to be executed at each client’s equipment. The theoretical proof is also carried out to show how much DP can be attained by use of the aforementioned randomized DP matrix factorization algorithm. Finally, extensive numerical studies are presented to evaluate the effectiveness of our proposed novel algorithms using both simulated and real datasets for building the FeMRSs.