## 1 Introduction  
With the rapid growth of various network platforms, the explosive growth of information has made it difficult for users to rapidly seek targets. To alleviate the information overload problem, recommendation systems have developed rapidly. Classical CF recommendation method is widely used to alleviate information overload. CF takes the historical behaviour data of users as input to calculate the similarity between them, so as to predict the preference of users [1, 2, 3]. However, traditional CF cannot effectively solve the data sparsity. To this end, matrix factorization (MF) assumes that users have some latent factors with itemss, so establishes a low-dimensional dense representation space for users and items and then compares them in the common vector space. MF uses the dot product to acquire the similarity for user-items and then recommend items with high similarity to target users [4]. Generally, there are complex nonlinear mapping relationships between the original representation space and low-dimensional dense representation space for user-items. To better research the nonlinear relationships, researchers learn from the ideas of deep learning [5] and machine learning [6], and apply them to recommendation systems [7, 8]. [PERSON] et al. [9] proposed the Deep Structured Semantic Models (DSSM), which utilizes a DNN to express search keywords and clicked text titles as low-dimensional dense representation vectors and calculates the distance between the two dense representation vectors through cosine similarity. Inspired by DSSM, [PERSON] et al. [10] proposed a Deep Matrix Factorization (DMF), which uses two-pathway DNNs instead of linear embedding as interaction function, learns the common low-dimensional dense representation space for user-items and makes use of the inner product as a predictive function to make rating predictions. Not only can DNNs learn more accurate user-item representations, but since DNNs can theoretically fit any continuous function, they are well-suited for learning complex matching functions [11; 12]. For instance, [PERSON] et al. proposed the NeuMF model which takes the concatenation of user-item representations as the input of MLP and uses a multilayer neural network as the interaction function [13]. Although DNNs are characterized by high capacity and nonlinearity, an MLP is difficult in capturing low-rank relationships as revealed by [PERSON] et al. [14]. The CF methods based on matching function learning use an MLP to explore user-item interaction. Generally, humans cannot process the whole signal at once but can only selectively focus on part of the signal content, hence, the attention mechanism is derived [15; 16]. Attention mechanisms have been widely applied to many fields [17] such as recommendation systems [18; 19] that start from data processing. The models apply attention mechanism to automatically find the key points of the input vectors and distribute corresponding weights to the input to optimize the traditional recommendation model. For instance, [PERSON] et al. proposed the AFM model [20]. By introducing the attention mechanism into the enhanced FM model, AFM learns by assigning weights to different feature combinations and uses the attention network to update the weights to achieve performance improvements. In brief, the methods based on MF are good at learning the low-rank relationships for user-items, but they are difficult to capture the nonlinear relationships for user-items due to using linear interaction functions. The methods based on MLP can capture the nonlinear relationship but have disadvantages in learning low-rank relationships. These two methods have different advantages in different perspectives. In order to effectively coordinate the flexibility of learning complex matching functions and user-item low-rank relationships, we propose a Deep Collaborative Recommendation Algorithm based on Attention Mechanism (DACR).