# Modeling Implicit Trust in Matrix Factorization-Based Collaborative Filtering
###### Abstract  
Recommendation systems often use side information to both alleviate problems, such as the cold start problem and data sparsity, and increase prediction accuracy. One such piece of side information, which has been widely investigated in addressing such challenges, is trust. However, the difficulty in obtaining explicit relationship data has led researchers to infer trust values from other means such as the user-to-item relationship. This paper proposes a model to improve prediction accuracy by applying the trust relationship between the user and item ratings. Two approaches to implement trust into prediction are proposed: One involves the use of estimated trust, and the other involves the initial trust. The efficiency of the proposed method is verified by comparing the obtained results with four well-known methods, including the state-of-the-art deep learning-based method of neural graph collaborative filtering (NGCF). The experimental results demonstrate that the proposed method performs significantly better than the NGCF, and the three other matrix factorization methods, namely, the singular value decomposition (SVD), SVD++, and the social matrix factorization (SocialMF). recommendation system; collaborative filtering; matrix factorization; SVD++; implicit trust; latent factor model +
Footnote †: journal: Medical  
regularization factor is used to prevent overfitting. The singular value decomposition (SVD) is imposed as a baseline for model-based CF. However, MF models are difficult to generalize to the data when the original rating matrix is sparse. Several approaches have been proposed to address this challenge. The simplest and most common approach to resolve the sparsity problem involves inputting artificial data into the original matrix, and mean ratings are often used for this purpose. To address the problems associated with data sparsity in low-rank matrix approximation, [PERSON] and [PERSON] [7] proposed a model that uses a weight inversely proportional to the noise variance. Similarly, [PERSON] et al. [8] proposed an approach, namely, local low-rank matrix approximation (LLORMA), which approximates the observed matrix as the weighted sum of local low-rank matrices that are targeted to the local regions of the observed matrix. To construct the final approximated matrix, several local models are aggregated. [PERSON] et al. [9] proposed a similar method referred to as divide-and-conquer (DFC) MF. In contrast to LLORMA, DFC uses overlapping partitions of the observed matrix to construct the local models. To improve the efficiency of recommendation systems, the use of side information has been widely researched. Apart from side information such as the context and user and item characteristics, trust is often used as a reliable measure to incorporate into the CF technique. However, obtaining the explicit trust link between users is difficult. Here, we propose a new trust measure that can be derived directly from the user's preference matrix. In contrast to most trust metrics, which measure the degree of reliability between two users, our proposed metrics measure the user's trust regarding the preference they have expressed. The metric consists of two components: (1) the user's proportional rating on the target item, and (2) item popularity. Then, the resulting trust metric is incorporated into predictions. We used two approaches to do so; one involves an estimation of the trust matrix from the initial trust values, and the second directly adds trust values into the prediction. CF models that perform optimization based on the prediction accuracy can be viewed as regression problems. The method proposed in the present work is likewise modeled as a regression problem. One of the most common evaluation metrics used for calculating the prediction accuracy in recommendation systems is the mean absolute error (MAE), which is based on the prediction error; in particular, the MAE indicates the mean absolute difference between the predicted value and the actual rating.