Many applications require the ability to identify data that is anomalous with respect to a target group of observations, in the sense of belonging to a new, previously unseen `attacker' class. One possible approach to this kind of verification problem is one-class classification, learning a description of the target class concerned based solely on data from this class. However, if known non-target classes are available at training time, it is also possible to use standard multi-class or two-class classification, exploiting the negative data to infer a description of the target class. In this paper we assume that this scenario holds and investigate under what conditions multi-class and two-class Na