# Social Recommendation Based on Quantified Trust and User's Primary Preference Space
## 2 Related Work  
In this section, we briefly review the related work of social recommendation methods.  
The memory-based social recommendation method uses a trust network to supplement the rating data and predicts the users' ratings according to the ratings from their trusted friends or the similar users. [PERSON] et al. [4] proposed a random walk model that combines trust and collaborative filtering methods for recommendation. [PERSON] et al. [24] used trust data instead of rating data to find neighboring users. [PERSON] [25] combined collaborative filtering methods with an optimized clustering method to cluster users by users' similarity and trust relationships. Although the methods above effectively alleviate the sparsity problem and the cold-start problem, the time complexity of the algorithm also increases due to the added search strategy. Furthermore, these methods have low scalability and are not suitable for big data scenarios.  
Model-based techniques are used to \"guess\" to what extent a user will like a new item and utilize several machine learning algorithms to train on the vector of items for a specific user, then they can build a model that can predict the user's rating for a new item that has just been added to the system. As a typical model-based social recommendation method, the probability matrix factorization method can use low-dimensional vectors to represent users' preferences for items and train prediction models based on rating data and trust data [2; 3; 8; 9]. [PERSON] et al. [23] used probability matrix factorization to model trust network information and rating information. [PERSON] et al. [7] modeled users as trustees and trusted individuals, respectively. [PERSON] et al. [10] used network embedding, rather than PMF (probabilistic matrix factorization), and not with RWR (random walk with restart) to quantify users' trust. [PERSON] et al. [26] used the dual graph attention network and proposed a new policy-based fusion strategy based on contextual multi-armed bandit to weigh interactions of various social effects. [PERSON] et al. [27] designed a special feature evolution unit that enabled the embedding vectors for two tasks to exchange their features in a probabilistic manner, and further harness a meta-controller to globally explore proper settings for the feature evolution units. Although SREPS [10], DANSER [26] and TrustEV [27] have achieved good results to a certain extent, the time efficiency of the graph embedding method used by SREPS and the graph neural network method used by DANSER and TrustEV are very low.  
The social recommendation algorithm based on probability matrix factorization not only possesses the advantages of the scalability of the matrix factorization method [8; 9], but also utilizes social information to achieve higher accuracy. However, the trust data used by these social recommendation methods are binary data; it can only reflect whether there is a trust relationship between users and friends, but can not distinguish the strength of these friends. When we only use binary data for recommendation, we can only randomly select friends with trust relationship to assist in recommendation, and so can not find the most similar friends (because their trust values are all 1). On the contrary, when we quantify the trust data, we can easily refer to the most similar friend to make a more accurate recommendation. This motivates us to propose a new framework.