  Pairwise similarities and dissimilarities between data points might be easier
to obtain than fully labeled data in real-world classification problems, e.g.,
in privacy-aware situations. To handle such pairwise information, an empirical
risk minimization approach has been proposed, giving an unbiased estimator of
the classification risk that can be computed only from pairwise similarities
and unlabeled data. However, this direction cannot handle pairwise
dissimilarities so far. On the other hand, semi-supervised clustering is one of
the methods which can use both similarities and dissimilarities. Nevertheless,
they typically require strong geometrical assumptions on the data distribution
such as the manifold assumption, which may deteriorate the performance. In this
paper, we derive an unbiased risk estimator which can handle all of
similarities/dissimilarities and unlabeled data. We theoretically establish
estimation error bounds and experimentally demonstrate the practical usefulness
of our empirical risk minimization method.
