ABSTRACT Recently, convolutional neural networks (CNNs) have achieved excellent performance for the recommendation system by extracting deep features and building collaborative filtering models. However, CNNs have been verified susceptible to adversarial examples. This is because adversarial samples are subtle non-random disturbances, which indicates that machine learning models produce incorrect outputs. Therefore, we propose a novel model of Adversarial Neural Collaborative Filtering with Embedding Dimension Correlations, named ANCF in short, to address the adversarial problem of CNN-based recommendation system. In particular, the proposed ANCF model adopts the matrix factorization to train the adversarial personalized ranking in the prediction layer. This is because matrix factorization supposes that the linear interaction of the latent factors, which are captured between the user and the item, can describe the observable feedback, thus the proposed ANCF model can learn more complicated representation of their latent factors to improve the performance of recommendation. In addition, the ANCF model utilizes the outer product instead of the inner product or concatenation to learn explicitly pairwise embedding dimensional correlations and obtain the interaction map from which CNNs can utilize its strengths to learn high-order correlations. As a result, the proposed ANCF model can improve the robustness performance by the adversarial personalized ranking, and obtain more information by encoding correlations between different embedding layers. Experimental results carried out on three public datasets demonstrate that the ANCF model outperforms other existing recommendation models.