This paper proposes several methods for training a Convolutional Neural Network (CNN) for learning the similarity between images of silk fabrics based on multiple semantic properties of the fabrics. In the context of the EU H2020 project SILKNOW (http://silknow.eu/), two variants of training were developed, one based on a Siamese CNN and one based on a triplet architecture. We propose different definitions of similarity and different loss functions for both training strategies, some of them also allowing the use of incomplete information about the training data. We assess the quality of the trained model by using the learned image features in a k-NN classification. We achieve overall accuracies of 93-95% and average F1-scores of 87-92%. © 2020 Copernicus GmbH. All rights reserved.