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.

该论文提出了一种利用成对数据信息进行分类的方法，其中使用了经验风险最小化方法来评估分类风险，可以从成对相似性和未标记数据计算出分类风险的无偏估计器。这种方法不仅可以处理相似性，而且还可以处理不相似性，并且可以估计误差范围。

通过经验风险最小化从成对相似性/不相似性和无标签数据中进行分类