# Weighted Matrix Factorization Recommendation Model Incorporating Social Trust
## 2 Related Work  
The primary purpose of incorporating social networks is to utilize the trust relationships between users to alleviate the problem of data sparsity. In 2008, [PERSON] et al. (2008) proposed the SoRec model, which is based on probabilistic matrix factorization. It captures the feature vectors of both users and items by jointly considering the user rating matrix and the social network. In this model, a user's feature vector is influenced not only by their own ratings but also by those they trust. The experimental results show that this model performs well in prediction accuracy, especially when users have few or no ratings, indicating that integrating users' social network information into the recommendation model can significantly improve the accuracy of recommendations. Different from the way SoRec constructs social information, [PERSON] et al. (2008) proposed the TrustMF model, which starts from the genesis of trust relationships and models both trusting and being trusted behaviors separately. Experimental results demonstrate that considering the impact of user roles (trustor and trustee) in social recommendations effectively improves recommendation performance. [PERSON] et al. (2008) believe that a user's ratings for items are influenced not only by their own preferences but also by those they trust. They proposed the RSTE model based on matrix factorization, which expresses a user's rating for an item as the linear sum of two parts: the individual's ratings for the item and the ratings given by those they trust. However, this model only considers the influence of trusted users on user ratings, neglecting their impact on user feature vectors. [PERSON] et al. (2008) argue that users and their trusted users have similar feature vectors, and the similarity between these vectors depends on the user's degree of trust in their trusted users. They introduced the SocialMF model based on trust propagation, where a user's feature vector equals the average feature vector of their trusted users. Experiments show that trust propagation can effectively solve the cold start problem and significantly improve recommendation accuracy. Later, [PERSON] et al. (2008) introduced SoReg, a model with a similar concept to SocialMF, assuming that a user's feature vector should be similar to their friends' feature vectors, but this model uses social information to regularize user feature vectors. [PERSON] et al. (2008) believe that not only explicit user ratings and social relationships should be modeled but also users' implicit behavior data and social relationships. Therefore, they introduced implicit social information into the SVD++ model ([PERSON] et al., 2008), creating the TrustSVD model. By considering users' implicit feedback and implicit social information in the model, the representation of a user's features relies not only on the user feature vector but also on implicit feedback and implicit friend information, making the feature representation more consistent with real-world scenarios. [PERSON] et al. (2008) proposed a new data imputation model that uses social networks to fill in missing parts of the user-item matrix, thereby reducing data sparsity. In recent years, deep learning methods have gradually been integrated into recommendation models. [PERSON] et al. (2016) proposed a matrix factorization model combined with neural networks, NeuMF, which takes the embeddings of users and items as input. This model processes these inputs through two parallel structures: one part uses Generalized Matrix Factorization (GMF) to learn the linear relationships between users and items and the other part uses a multi-layer perceptron to learn the nonlinear relationships between them. Then, the outputs of these two parts are combined and passed through a neural network layer for final prediction. This approach, combining linear and nonlinear models,can better model the complex interactions between users and items in recommendation systems, thereby improving the accuracy of recommendations. [PERSON] et al.