  We consider the unsupervised learning problem of assigning labels to
unlabeled data. A naive approach is to use clustering methods, but this works
well only when data is properly clustered and each cluster corresponds to an
underlying class. In this paper, we first show that this unsupervised labeling
problem in balanced binary cases can be solved if two unlabeled datasets having
different class balances are available. More specifically, estimation of the
sign of the difference between probability densities of two unlabeled datasets
gives the solution. We then introduce a new method to directly estimate the
sign of the density difference without density estimation. Finally, we
demonstrate the usefulness of the proposed method against several clustering
methods on various toy problems and real-world datasets.
