In this paper, we propose a two-step method to normalize multi-word terms with concepts from a domain-specific ontology. Normalization is a critical step of information extraction. The method uses vector representations of terms computed with word embedding information and hierarchical information among ontology concepts. A training dataset and a first result dataset with high precision and low recall are generated by using the ToMap unsupervised normalization method. It is based on the similarities between the form of the term to normalize and the form of concept labels. Then, a projection of the space of terms towards the space of concepts is learned by globally minimizing the distances between vectors of terms and vectors of concepts. It applies multivariate linear regression using the previously generated training dataset. Finally, a distance calculation is carried out between the projections of term vectors and the concept vectors, providing a prediction of normalization by a concept for each term. This method was evaluated through the categorization task of bacterial habitats of BioNLP Shared Task 2016. Our results largely outperform all existing systems on this task, opening up very encouraging prospects.