  Positive unlabeled (PU) learning is useful in various practical situations,
where there is a need to learn a classifier for a class of interest from an
unlabeled data set, which may contain anomalies as well as samples from unknown
classes. The learning task can be formulated as an optimization problem under
the framework of statistical learning theory. Recent studies have theoretically
analyzed its properties and generalization performance, nevertheless, little
effort has been made to consider the problem of scalability, especially when
large sets of unlabeled data are available. In this work we propose a novel
scalable PU learning algorithm that is theoretically proven to provide the
optimal solution, while showing superior computational and memory performance.
Experimental evaluation confirms the theoretical evidence and shows that the
proposed method can be successfully applied to a large variety of real-world
problems involving PU learning.
