# Modeling Implicit Trust in Matrix Factorization-Based Collaborative Filtering
## 2 Related Work  
In this section, we discuss some related work on recommendation systems that use the trust relationship to improve accuracy. [PERSON] and [PERSON] [10] reported on one of the earliest attempts to use trust in a recommender system. Inspired by the PageRank algorithm [10], the authors used trust propagation in the network to estimate the trust matrix. However, a drawback of this model was that it combined the similarity matrix with the trust matrix, thereby increasing the computational time and dependence on the similarity matrix. [PERSON] [11] designed a model for movie recommendation, named TidalTrust, which uses social trust, i.e., trust inferred from a social network. The concept behind this model is that people prefer recommendations from acquaintances or friends instead of from relatively unknown people. Trust is defined as one's commitment to act in the future, in such a way that leads to a positive outcome for the one who relies on the committed action; it is calculated using a modified version of the breadth-first search. In the prediction phase, the calculated trust is used to weight the ratings of the neighbors. In [12], [PERSON] proposed a trust model, in which trust is inferred as the target user's contribution to the prediction accuracy. In contrast to all the other models discussed in this section, this model does not depend on explicit social links to infer trust. However, this model has considerably higher computation costs because of the initial prediction calculation during the trust matrix generation. Addressing these issues with prediction accuracy-based trust models, [PERSON] et al. [13] proposed AgreeRelTrust, which is a model that uses the agreement between users to infer trust, eliminating the need to calculate the initial predictions. This method also takes into account the activeness of the users when calculating the trust; however, the method is a memory-based model, and is thus not as computationally efficient as the MF variants. [PERSON] et al. [14] used an SVD sign-based community mining method to discover trust and distrust to improve the accuracy of the CF-based recommendation system. The users in the system are first clustered into k communities. The rationale behind clustering users is that users within the same community tend to share a positive relationship, whereas a negative relationship exists between different communities. Although the method improves the accuracy of the recommendations, the trust mining method uses a binary trust value to indicate trust and distrust. Owing to the binary nature of the implicit rating, most trust-based recommenders that rely on the Pearson similarity fail. SVD++, an extension of SVD, takes auxiliary information such as the users' historical consumption [15] and combines the neighborhood method with MF. However, the model is limited to user-side implicit feedback, ignoring the item side, and treats all implicit feedback equally. Another line of research that has recently gained popularity is graph-based recommendation, in which the model relies on a bipartite graph generated from user interactions. In a recent work, [PERSON] et al. [16] proposed graph-based collaborative filtering (GCF), addressing the issues imposed by SVD++. The recommendation process is modeled as a bipartite graph structure, considering both item-side and user-side implicit feedback. [PERSON] et al. [17] proposed a general graph-based framework for top-N recommendations (GraFC2T2) that accounts for several side information aspects, including trust. First, the graph structure is constructed from the data, and is then used to make recommendations. The graph structure captures both the content-based features and edge weight time. The PageRank algorithm [18] runs on the graph to make recommendations, and the final recommendations are updated based on the trust between user pairs. This trust integration uses both explicit and implicit trust. The key advantage of GraFC2T2 is that it is a highly modular framework. In contrast, in the method proposed by [PERSON] et al.