Novelty detection is an important tool for unsupervised data analysis. It relies on finding regions of low density within which events are then flagged as novel. By design this is dependent on the underlying measure of the space. In this paper we derive a formulation which is able to address this problem by allowing for a reference measure to be given in the form of a sample from an alternative distribution. We show that this optimization problem can be solved efficiently and that it works well in practice.