  Maximizing the area under the receiver operating characteristic curve (AUC)
is a standard approach to imbalanced classification. So far, various supervised
AUC optimization methods have been developed and they are also extended to
semi-supervised scenarios to cope with small sample problems. However, existing
semi-supervised AUC optimization methods rely on strong distributional
assumptions, which are rarely satisfied in real-world problems. In this paper,
we propose a novel semi-supervised AUC optimization method that does not
require such restrictive assumptions. We first develop an AUC optimization
method based only on positive and unlabeled data (PU-AUC) and then extend it to
semi-supervised learning by combining it with a supervised AUC optimization
method. We theoretically prove that, without the restrictive distributional
assumptions, unlabeled data contribute to improving the generalization
performance in PU and semi-supervised AUC optimization methods. Finally, we
demonstrate the practical usefulness of the proposed methods through
experiments.
