Distance/Similarity learning is a fundamental problem in machine learning. For example, kNN classifier or clustering methods are based on a distance/similarity measure. Metric learning algorithms enhance the efficiency of these methods by learning an optimal distance function from data. Most metric learning methods need training information in the form of pair or triplet sets. Nowadays, this training information often is obtained from the Internet via crowdsourcing methods. Therefore, this information may contain label noise or outliers leading to the poor performance of the learned metric. It is even possible that the learned metric functions perform worse than the general metrics such as Euclidean distance. To address this challenge, this paper presents a new robust metric learning method based on the Rescaled Hinge loss. This loss function is a general case of the popular Hinge loss and initially introduced in Xu et al. (Pattern Recogn 63:139–148, 2017) to develop a new robust SVM algorithm. In this paper, we formulate the metric learning problem using the Rescaled Hinge loss function and then develop an efficient algorithm based on HQ (Half-Quadratic) to solve the problem. Experimental results on a variety of both real and synthetic datasets confirm that our new robust algorithm considerably outperforms state-of-the-art metric learning methods in the presence of label noise and outliers.

距离/相似性学习是机器学习中的一个基本问题。例如，kNN分类器或聚类方法基于距离/相似性度量。度量学习算法通过从数据中学习最佳距离函数来提高这些方法的效率。大多数度量学习方法都需要成对或三联集形式的训练信息。如今，这种培训信息通常是通过众包方法从Internet获得的。因此，此信息可能包含标签噪声或异常值，从而导致学习的度量标准的性能不佳。甚至有可能学到的度量函数的性能比诸如欧几里得距离之类的常规度量更差。为了解决这一挑战，本文提出了一种基于重标铰链损失的新的鲁棒度量学习方法。这种损失函数是普遍的铰链损失的一般情况，最初是在Xu等人中引入的。（Pattern Recogn 63：139–148，2017）开发一种新的鲁棒SVM算法。在本文中，我们使用重新缩放的铰链损失函数来制定度量学习问题，然后开发一种基于HQ（半二次方）的有效算法来解决该问题。在各种真实和合成数据集上的实验结果证实，在存在标签噪声和异常值的情况下，我们的新鲁棒算法大大优于最新的度量学习方法。我们使用Rescaled Hinge损失函数来制定度量学习问题，然后开发一种基于HQ（半二次方）的有效算法来解决该问题。在各种真实和合成数据集上的实验结果证实，在存在标签噪声和异常值的情况下，我们的新鲁棒算法大大优于最新的度量学习方法。我们使用Rescaled Hinge损失函数来制定度量学习问题，然后开发一种基于HQ（半二次方）的有效算法来解决该问题。在各种真实和合成数据集上的实验结果证实，在存在标签噪声和异常值的情况下，我们的新鲁棒算法大大优于最新的度量学习方法。