Click-through rate prediction is critical in Internet advertising and affects web publisher's profits and advertiser's payment. The traditional method of obtaining features using feature extraction did not consider the sparseness of advertising data and the highly nonlinear association between features. To reduce the sparseness of data and to mine the hidden features in advertising data, a method that learns the sparse features is proposed. Our method exploits dimension reduction based on decomposition, takes advantage of the attention mechanism in neural network modelling, and improves FM to make feature interactions contribute differently to the prediction. We utilize stack autoencoder to explore high-order feature interactions and use improved FM for low-order feature interactions to portray the nonlinear associated relationship of features. The experiment shows that our method improves the effect of CTR prediction and produces economic benefits in Internet advertising.