A number of important applied problems in engineering, finance and medicine can be formulated as a problem of anomaly detection based on a one-class classification. A classical approach to this problem is to describe a normal state using a one-class support vector machine. Then to detect anomalies we quantify a distance from a new observation to the constructed description of the normal class. In this paper we present a new approach to one-class classification. We formulate a new problem statement and a corresponding algorithm that allow taking into account privileged information during the training phase. We evaluate performance of the proposed approach using synthetic datasets, as well as the publicly available Microsoft Malware Classification Challenge dataset.