In most real world scenarios, experts dispose of limited background knowledge that they can exploit for guiding the analysis process. In this context, semi-supervised clustering can be employed to leverage such knowledge and enable the discovery of clusters that meet the analysts’ expectations. To this end, we propose a semi-supervised deep embedding clustering algorithm that exploits triplet constraints as background knowledge within the whole learning process. The latter consists in a two-stage approach where, initially, a low-dimensional data embedding is computed and, successively, cluster assignment is refined via the introduction of an auxiliary target distribution. Our algorithm is evaluated on real-world benchmarks in comparison with state-of-the-art unsupervised and semi-supervised clustering methods. Experimental results highlight the quality of the proposed framework as well as the added value of the new learnt data representation.