On simple one-class classification methods

The one-class classification has been successfully applied in many communication, signal processing, and machine learning tasks. This problem, as defined by the one-class SVM approach, consists in identifying a sphere enclosing all (or the most) of the data. The classical strategy to solve the problem considers a simultaneous estimation of both the center and the radius of the sphere. In this paper, we study the impact of separating the estimation problem. It turns out that simple one-class classification methods can be easily derived, by considering a least-squares formulation. The proposed framework allows us to derive some theoretical results, such as an upper bound on the probability of false detection. The relevance of this work is illustrated on well-known datasets.