Data domain description techniques aim at deriving concise descriptions of objects belonging to a category of interest. For instance, the support vector domain description (SVDD) learns a hypersphere enclosing the bulk of provided unlabeled data such that points lying outside of the ball are considered anomalous. However, relevant information such as expert and background knowledge remain unused in the unsupervised setting. In this paper, we rephrase data domain description as a semi-supervised learning task, that is, we propose a semi-supervised generalization of data domain description (SSSVDD) to process unlabeled and labeled examples. The corresponding optimization problem is non-convex. We translate it into an unconstraint, continuous problem that can be optimized accurately by gradient-based techniques. Furthermore, we devise an effective active learning strategy to query low-confidence observations. Our empirical evaluation on network intrusion detection and object recognition tasks shows that our SSSVDDs consistently outperform baseline methods in relevant learning settings.