With the proliferation of social media platforms and e-commerce sites, several cross-domain collaborative filtering strategies have been recently introduced to transfer the knowledge of user preferences across domains. The main challenge of cross-domain recommendation is to weigh and learn users' different behaviors in multiple domains. In this paper, we propose a Cross-Domain collaborative filtering model following a Translation-based strategy, namely CDT. In our model, we learn the embedding space with translation vectors and capture high-order feature interactions in users' multiple preferences across domains. In doing so, we efficiently compute the transitivity between feature latent embeddings, that is if feature pairs have high interaction weights in the latent space, then feature embeddings with no observed interactions across the domains will be closely related as well. We formulate our objective function as a ranking problem in factorization machines and learn the model's parameters via gradient descent. In addition, to better capture the non-linearity in user preferences across domains we extend the proposed CDT model by using a deep learning strategy, namely DeepCDT. Our experiments on six publicly available cross-domain tasks demonstrate the effectiveness of the proposed models, outperforming other state-of-the-art cross-domain strategies.