Pairwise similarities and dissimilarities between data points are often obtained more easily than full labels of data in real-world classification problems. To make use of such pairwise information, an empirical risk minimization approach has been proposed, where an unbiased estimator of the classification risk is computed from only pairwise similarities and unlabeled data. However, this approach has not yet been able to handle pairwise dissimilarities. Semisupervised clustering methods can incorporate both similarities and dissimilarities into their framework; however, they typically require strong geometrical assumptions on the data distribution such as the manifold assumption, which may cause severe performance deterioration. In this letter, we derive an unbiased estimator of the classification risk based on all of similarities and dissimilarities and unlabeled data. We theoretically establish an estimation error bound and experimentally demonstrate the practical usefulness of our empirical risk minimization method.

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