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Recently, some attempts have been made in introducing deep neural networks (DNNs) to recommender systems for generating more accurate prediction due to the nonlinear representation learning capability of DNNs. However, they inevitably result in high computational and storage costs. Worse still, due to the relatively small number of ratings that can be fed into DNNs, they may easily suffer from the overfitting issue. To tackle these issues, we propose a novel recommendation framework based on Back Propagation (BP) neural network with attention mechanism, namely BPAM++. In particular, the BP neural network is utilized to learn the complex relationship between the target user and his/her neighbors and the complex relationship between the target item and its neighbors. Compared with DNNs, the shallow neural network, i.e., BP neural network, can not only reduce the computational and storage costs, but also alleviate the overfitting issues in DNNs caused by a relatively small number of ratings. In addition, an attention mechanism is designed to capture the global impact of the nearest users of the target user on their nearest target user sets. Extensive experiments conducted on eight benchmark datasets confirm the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]