A challenge in using machine learning for tasks such as network intrusion detection and fault diagnosis is the difficulty in obtaining clean data for training in order to model the normal behavior of the system. Unsupervised anomaly detection techniques such as one class support vector machines (SVMs) have been introduced to overcome this difficulty. One class support vector machines model the normal or target data using non-linear surfaces in the input space while ignoring the anomalous data. Our approach to this problem is based on fitting a hyperellipsoid with a minimal effective radius, centered at the origin, around a majority of the data vectors in a higher dimensional space. We formulate this as a linear optimisation problem, which is advantageous in terms of its computational complexity. We demonstrate using real data from the great duck Island Project that our approach achieves better detection performance and flexibility in terms of parameter selection, compared to an earlier detection scheme using a quarter sphere SVM.