  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. 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.
