Social network recommendation based on low-rank matrix decomposition

Social network data can facilitate delivering personalized and relevant content to users, but at the same time, poses challenges for designing effective recommendation algorithms that need to handle user preferences, ratings, comments, and other social information. In this study, we leverage social network information to improve the accuracy and efficiency of recommendation systems. We propose two algorithms: Social Network Regularized Kernel Norm Minimization (SNRKNM) based on low- rank matrix factorization techniques and Fuzzy Radial Basis Function Low-Rank Matrix Factorization (FRLRMF), which can utilize social network information more effectively and efficiently. We evaluate and compare these algorithms with two traditional methods: a matrix factorization-based algorithm (the Stochastic Gradient Descent Algorithm Based on Collaborative Filtering (SGD)) and a social net- work algorithm (Social Network Based Collaborative Filtering Recommendation Algorithm (SNCR)), tested on synthetic datasets and the real-world MovieLens dataset. On the MovieLens dataset, our algorithms achieve a root mean square error (RMSE) of 0.74, significantly outperforming the base- line SGD recommendation algorithm’s 1.11, statistically significant at the 0.01 level. Compared to the baseline, our algorithms reduce RMSE by 36.28% and exhibit high scalability and robustness across different dataset sizes and rank parameters. SNRKNM utilizes kernel norm smoothing on the latent factors of users and items, capturing their social similarities and diversities. FRLRMF embeds the fuzzy memberships of users and items into the radial basis function (RBF) kernel, handling uncertainty and noise in social network data. In contrast, the SNCR algorithm relies on collaborative filtering within the social network but has limitations in handling large-scale datasets and sparsity. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.