# Social Recommendation Based on Quantified Trust and User's Primary Preference Space
###### Abstract  
Social recommendation has received great attention recently, which uses social information to alleviate the data sparsity problem and the cold-start problem of recommendation systems. However, the existing social recommendation methods have two deficiencies. First, the binary trust network used by current social recommendation methods cannot reflect the trust level of different users. Second, current social recommendation methods assume that users only consider the same influencial factors when purchasing goods and establishing friendships, which does not match the reality, since users may have different preferences in different scenarios. To address these issues, in this paper, we propose a novel social recommendation framework based on trust and preference, named TPSR, including a trust quantify method based on random walk with restart (TQ_RWR) and a user's primary preference space model (UPPS). Our experimental results in four public real-world datasets show that TQ_RWR can improve the utilization of trust information, and improve the recommended accuracy. In addition, compared with current social recommendation methods/studies, TPSR can achieve a higher performance in different metrics, including root mean square error, precision, recall and F1 value. recommendation system; collaborative filtering; trust network; matrix factorization Article  
Social Recommendation Based on  
Primary Preference Space. _Appl. Sci._**2022**, 12141. [[https://doi.org/10.3390/app122312141](https://doi.org/10.3390/app122312141)]([https://doi.org/10.3390/app122312141](https://doi.org/10.3390/app122312141))  
Academic Editor: [PERSON]  
Received: 1 November 2022  
Accepted: 24 November 2022  
Published: 27 November 2022  
**Published: 27 November 2022**  
data sparsity and cold-start problems lead to inaccurate modeling of users or items, which further reduces the recommendation accuracy [20; 21]. Incorporating social information into the recommendation method is one of the effective ways to solve the sparsity problem and cold-start problem [14; 22]. Connected users tend to have similar behavioral preferences, while people with similar behavioral preferences tend to establish connections [22]. Thus, when lacking users' historical rating data, the history of their friends can be used to make recommendations for them. Due to its effectiveness in alleviating the sparsity and cold-start problems, social recommendation methods combined with social information have attracted much attention in recent years. Social recommendation based on probability matrix decomposition, in particular, has the advantages of the scalability of the matrix decomposition method with higher accuracy by introducing social information [8; 9]. Although current social recommendation can effectively alleviate the sparsity and the cold-start problems, we identify two more problems. First, the trust networks with social information used by the current social recommendation methods are binary data. They only use the local information of the network, the direct trust relationship between users, and ignore the overall structure information of the network [7; 23]. Second, when the social recommendation methods model trust data and rating data, it is considered that the trust evaluation and the rating share the same preference space. However, users normally consider different factors when rating items and when developing social relationships. For example, the rating of the items may be influenced by many factors, such as product quality, brand, appearance, etc. In terms of whether to develop trust relationships with others, users may consider many factors, such as a user's occupation, personality and background. This paper proposes a novel social recommendation framework, named TPSR, to solve the two issues identified.