With the development of Internet technology, the amount of network information has increased rapidly, resulting in information overload. The problem of information overload renders users unable to obtain effective information quickly ^{[1][2][3][4][5][6]}[1,2,3,4,5,6]. A recommendation system [7] has an excellent effect in addressing this problem. A recommender system is an online personalized recommendation system that helps users find and recommend items of interest by searching, and analyzing user preferences ^[8][9][8,9]. Currently, the main methods for recommender systems to learn user preferences fall into three categories ^[10][11][10,11]: content-based methods [12], collaborative filtering methods ^{[13][14][15][16][17][18][19][20][21]}[13,14,15,16,17,18,19,20,21], and hybrid recommendation methods [22]. In essence, these algorithms solve the common problems of data sparsity, data scalability, and cold starts in recommender systems from different perspectives. For instance, Gulzar et al. [23] proposed a new clustering algorithm based on an ordered clustering algorithm (OCA), which aims to reduce the impact of cold starts, and data sparsity. Wu et al. [24] proposed the sampled SoftMax (SSM) loss as an efficient substitute for SoftMax loss, which can optimize long-tail recommendation.

Collaborative filtering is a popular recommendation algorithm. Based on the user behavior data (such as the ratings of users over items, user comments on items, and so on), it determines the correlation between users and items to provide personalized recommendations for users. The model-based recommendation is the most common collaborative filtering algorithm. Especially in recent years, models integrating an attention mechanism have become a research hotspot in the field of recommendation systems. The basic principle of the attention mechanism imitates the human visual system to assign different weights when processing information at different positions in the input sequence.

More and more researchers have integrated an attention mechanism to different degrees to solve the problems of data sparsity, data scalability, and cold starts.

Wang et al. [25] proposed a multi-attention deep neural network (MADNN) recommendation model based on embedding, and matrix factorization that can effectively alleviate data sparsity and cold start problems. The model enhances the interactivity of user/item embedding through a multi-attention mechanism. However, the dimensions of interactive user/item embeddings must be consistent, which may cause information loss caused by the number of features of different users, and items embedded into the same dimension.

Zhang et al. [26] proposed a probabilistic matrix factorization recommendation for self-attention mechanism convolutional neural networks with item auxiliary information, which can solve the problem of data sparsity in recommendation systems. The model adds a self-attention mechanism to the convolutional layer to establish the interaction between the auxiliary information of different channels. However, there is also the limitation that the dimensions of the auxiliary information of different channels must be consistent.

2. Matrix Factorization Recommendation Algorithm Based on Attention Interaction

Collaborative filtering algorithms based on matrix factorization (MF) are widely used, owing to their simplicity and ease of implementation. However, the rating matrix obtained by MF generally has the features of highly sparse data and uneven distribution, which lead to problems such as low recommendation performance, cold starts, and long tails ^[27][28][27,28]. To solve these problems, many researchers have proposed improved MF algorithms. Koren et al. [14] proved that a latent factor vector can enhance the ability of a model to deal with coefficient features. Badrul et al. [29] proposed singular value decomposition (SVD) to learn a user–item rating information matrix. However, the MF model learned using SVD was prone to overfitting. Subsequently, Funk [30] proposed the FunkSVD model, which adds a regularizer to the conventional SVD method to avoid overfitting the MF model. Koren et al. [14] Proposed a BiasSVD model with a bias term to solve the problem of large fluctuations in user-rating information. Based on BiasSVD, Koren ^[31][32][31,32] proposed the SVD++ model with implicit information to solve the cold-start problem caused by score sparsity. The abovementioned improved matrix factorization algorithm achieved excellent results in solving the sparsity problem of user–item rating information. Nevertheless, the simple vector dot product cannot establish a nonlinear relationship between the latent features of users and items, and the user and item features may not make full use of the latent space, leading to limited recommendation performance. Deep learning combined with matrix factorization has gradually become a mainstream research topic because of its nonlinear expression ability to establish a model. Li et al., [33] proposed a POI recommendation method fusing auxiliary attribute information based on the neural matrix factorization, integrating the convolutional neural network and attention mechanism (NueMF-CAA) to alleviate the data-sparsity problem. He et al., [34] introduced neural networks based on generalized matrix factorization (GMF). To express the nonlinear relationship between latent features, Tian et al. [35] proposed a deep matrix factorization (DMF) model that combines deep neural networks and matrix factorization techniques. DMF adds multiple hidden layers after the fully connected layers of the neural network to model higher-order interactions between users and items. Deep neural networks (DNNs) establish nonlinear relationships using weighted summation and reactivation, which may not highlight the key feature information. Therefore, the fusion of deep neural networks and attention mechanisms [36] has become a popular research topic. Wang et al. [37] proposed a convolutional neural network model based on the attention mechanism for CAPTCHA recognition, and their experimental results showed that the accuracy of CAPTCHA recognition was 93.27%. He et al. [38] proposed the inner attention-based recurrent neural network GATE function (IARNN-GATE), which uses the attention mechanism in the gate function of an RNN to control the information transmission of states between the hidden layers. Zhou et al. [39] proposed a recurrent neural network–attention mechanism model (RNN-AM) for microblog sentiment classification. Zhou et al. [40] proposed an image-denoising algorithm based on an attention mechanism and residual block, which effectively solved the problem of real image noise.