## 2 Related Work
### Cross-Domain User Social Relationships  
Cross-domain recommender systems (CDRSs) can assist recommendations in the target domain based on the knowledge learned from the source domain [41]. The existing cross-domain data fusion, respectively, fuses the users' characteristics in different storage sources, and user data from multiple platforms are further fused through the corresponding relationship of users to obtain the cross-domain data of users from multiple platforms. The existing cross-domain data mining methods use cross-domain user identification, cross-domain recommendations, and other methods to extract the value of cross-domain data [42; 43]. The cross-domain recommendation is proposed to solve the problem of data sparsity, and the rich training data in the source domain are used to improve the recommendation accuracy of the sparse domain. To improve the quality of recommendations, most of the existing cross-domain recommendation methods extract the domain-shared features among multiple related domains or integrate transfer learning with recommendation models. Some methods are based on matrix factorization (MF) and its variants, while others utilize clustering algorithms [44; 45; 46; 47]. [PERSON] et al. proposed a trust perception cross-domain deep neural matrix factorization (TCrossDNMF) model, which can address the user cold start problem in the cross-domain scenario of user overlap in the e-commerce system [48]. [PERSON] et al. aligned the potential factors between the two domains based on pattern matching and transferred the user preferences of the auxiliary domain to update the original user potential vector in the target domain [49]. [PERSON] et al. constructed a multi-graph according to user behavior in different fields and proposed a multi-graph neural network to learn cross-domain app embedding [50]. [PERSON] et al. designed a new framework, a deep adversarial and attention network (DAAN), which considers both domain-shared knowledge and domain-specific knowledge across domains [51]. Users' decisions are affected by personal preferences and social relationships at the same time, so some studies are based on the homogeneity hypothesis; that is, users connection to each other in social networks tend to have similar preferences [52]. [PERSON] et al. integrated user social networks into a random walk model with restart and conducted various tests on the internal correlation among group members to better describe group preferences and improved the performance of the group recommender system [53]. [PERSON] et al. proposed a social network recommendation method combining social tags and trust relationships [54]. Based on probability matrix factorization, major information related to social trust relationships, item tag information, and user rating matrix was collected, and all data resources from different dimensions were connected through shared user potential space (or item potential space). [PERSON] et al. proposed a unified framework to appropriately incorporate the influence of social relationships into the recommendations through the guidance of friends (friends who have a strong influence on users) and susceptibility (willingness to be affected) mining [55]. Traditional research on recommendations based on social relationships mostly focuses on analyzing the multifaceted impact of friends on user decisions and enriching user individual preferences. However, the structure of the social network has not changed. Although user purchases for others are taken into account, the recommendation algorithm has not been effectively applied. All the items of user historical behaviors are regarded as their preferences. As a result, when building the recommendation model, if there are items that do not belong to the users themselves, there may be a certain impact on the calculation of user preferences, reducing the accuracy of the recommendations.