Two alternative strategies addressing damage identification in structural health monitoring are presented in this contribution. Both strategies rely on reduced data representations - or features - to enable damage identification from vibrational data. To exploit a supervised learning scheme, training datasets are generated through numerical simulations, possibly speeded up through reduced order modelling. The first strategy deals with damage identification as a classification task employing onedimensional convolutional neural networks. Despite the good performance displayed in the proposed numerical benchmark of an eight-storey building, this approach suffers from the need of defining the possible damage classes a-priori, and from the lack of robustness of the extracted features. Both issues are successfully addressed by a second strategy, which relies on a Siamese architecture to learn a damage-sensitive low-dimensional metric space. In this second case, damage identification can be performed by solving a regression task in the learned metric space. This second approach is assessed against a test case involving a railway bridge, displaying impressive damage localization capabilities.