# Social)GCF: Social Recommendation with Jacobi Polynomial-Based Graph Collaborative Filtering
## 2 Problem and Related Work
### Related Work  
Due to the emergence of social networks, it is recognized that the user representation can be enhanced if the local neighbors of each user are considered [8; 9; 32]. Social recommendation systems have two main issues: the degree of influence by friends, which is also called social trust, and many trust-based methods have been proposed to infer trustworthy values for recommendation [33; 34; 35; 36], and user representation integration [9]. The trustworthy values between users and their connections indicate the degree of social influence. Many trust-based methods have been proposed to incorporate social trust into the recommendation system for better performance. DiffNet [7] assumes friends have equal influence by using mean-pooling. ESRF [5] adopts an autoencoder mechanism to filter unreliable social connections to improve recommendation accuracy.  
Normally, social recommendation systems involve two graphs, the user-item interaction graph and the social graph. Since both of them contain user representations, multiple methods have been proposed for combining user representation from the social graph and from the interaction graph, either creating a unified graph from these two graphs or simply fusing user representations from the two separate graphs.  
Unified graph approaches merge the social graph and interaction graph together and apply graph learning methods to the unified graph to learn node embeddings. DiffNet++ [13] captures both social influence and user interest in a unified graph and applies graph attention and diffusion layers to learn the final representations. HeteroGraphRec [37] treats the users and items as different types of nodes and social interactions and user-item interactions as different types of edges. Then, the social recommendation problem can be solved by learning representations from the heterogeneous graph.  
Compared with the unified graph approach, the dual graph approach is more flexible, since we can use different propagation depths for the two graphs and different models can be applied to the two graphs for better performance. DGRec [38] applied a graph attention network on the social graph which captures multi-hop social influences, and applied gated recurrent units on the user-item interaction sequences to capture the sequential patterns in user behavior. STGCN [39] uses graph convolution on the social graph to pretrain the user representations, which are then fine-tuned on the user-item interaction graph. For some dual graph approaches, the user representations from the social graph and user-item interaction graph should be effectively fused. In addition to the attention mechanism used in DGRec [38], a multi-layer perceptron can also be applied to the concatenated embedding vector to fuse the two representations [11; 40; 41; 42]. To effectively develop effective social recommendation systems which take the separate graph approach, the authors of [41] considered the co-occurrence frequency of item attributes to augment item embeddings. Despite the effectiveness of these methods, social recommendation systems still suffer in cold-start scenarios, where no or only a few interactions exist for a new user or item [24; 33; 40]. The comparisons with other papers are summarized in Table 1.