## 2 Related Works
### Matrix Factorization  
Matrix factorization (MF), one of the most commonly used models in collaborative filtering methods, uses a latent factor model to analyze rating information and identify users as well as item characteristics [16; 17]. The matrix factorization method factorizes the user rating matrix into two matrices: user latent factors and item latent factors; the inner product of the two matrices can help predict the rating of unrated items. Equation (1) represents the predicted rating of user \(u\) for item \(i\) (i.e., \(r^{*}_{u,i}\)):  
\[r^{*}_{u,i}=x^{T}_{i}\cdot y_{u} \tag{1}\]  
where \(x_{i}\) and \(y_{u}\) are the item latent factors and user latent factors, respectively. The ultimate goal of matrix factorization is to minimize the objective function-least square error, and find the best solution, as expressed in Equation (2). \[min_{x^{*},y}\sum_{(u,i)\in K}\left(r_{u,i}-x^{T}_{i}y_{u}\right)^{2}+\lambda \left(\|x_{i}\|^{2}+\|y_{u}\|^{2}\right) \tag{2}\]  
\(K\) is the set of implicit preferences of user \(u\) for product item \(i\), \(r_{u,i}\) represents the rating value of the training data, and \(r_{u,i}-x^{T}_{i}y_{u}\) presents the error between the actual rating and the predicted rating. To avoid overfitting, a constant \(\lambda\) is added to control the regularization. Matrix factorization models often use learning algorithms, such as Stochastic Gradient Descent (SGD) and Alternating Least Square (ALS), to tune models [16] and achieve the best prediction results. Users' text reviews can also be leveraged to analyze their preferences. [PERSON] et al. [37] coded user and product characteristics according to the contextual information of an article; they then modified the traditional matrix factorization model for rating prediction. [PERSON], [PERSON], [PERSON], and [PERSON] [9] applied the attention mechanism to a CNN to analyze the reviews of users and products and establish the latent factors of users and products, respectively. The matrix factorization method was then used to improve the accuracy of rating predictions. [PERSON], [PERSON], and [PERSON] [10] used CNN to analyze the word vectors in reviews and generate the vectors of latent factors for users and products, respectively; they then input the two feature vectors into the matrix factorization method to predict the ratings. The differentiating users' preferences and items' attractiveness (DUPIA) method uses a hybrid probabilistic matrix factorization model to predict user ratings based on diverse users' preferences extracted from auxiliary information [38]; it also uses attention in CNN to model products' textual attractiveness to different users in different perspectives of products. The latent factor model uses a user-item rating matrix to make predictions; however, such a matrix is commonly high-dimensional and sparse (HiDS). [PERSON] et al. [39] proposed an L\({}_{1}\)-and-L\({}_{2}\)-norm oriented latent factor (L\({}^{3}\)F) model, which aggregates L\({}_{1}\) norm-oriented Loss's robustness and L\({}_{2}\) norm-oriented Loss's stability; it well describes an HiDS rating matrix, and has high prediction accuracy, despite missing data in the matrix. The SGD-based latent factor analysis (LFA) model cannot handle a large-scale HiDS matrix due to the difficulty in tuning its learning rate. A P\({}^{2}\)SO-based LFA (PLFA) model [40] was proposed to efficiently construct a learning rate swarm in an SGD-based LFA model without any accuracy loss or computation burden. It also precisely presents an HiDS matrix, improves the prediction accuracy, and enhances computation efficiency. The latent factor model can also be used for quality-of-service (QoS) predictions. For example, a posterior-neighborhood-regularized latent factor (PLF) model constructs neighborhoods based on full information in a user-service matrix and has high accuracy of QoS prediction [41].