Latent embedding models are the basis of state-of-the art statistical solutions for modelling Knowledge Graphs and Recommender Systems. However, to be able to perform predictions for new entities and relation types, such models have to be retrained completely to derive the new latent embeddings. This could be a potential limitation when fast predictions for new entities and relation types are required. In this paper we propose approaches that can map new entities and new relation types into the existing latent embedding space without the need for retraining. Our proposed models are based on the observable - even incomplete - features of a new entity, e.g. a subset of observed links to other known entities. We show that these mapping approaches are efficient and are applicable to a wide variety of existing factorization models, including nonlinear models. We report performance results on multiple real-world datasets and evaluate the performances from different aspects.