  Metric learning aims to learn a distance metric such that semantically
similar instances are pulled together while dissimilar instances are pushed
away. Many existing methods consider maximizing or at least constraining a
distance margin in the feature space that separates similar and dissimilar
pairs of instances to guarantee their generalization ability. In this paper, we
advocate imposing an adversarial margin in the input space so as to improve the
generalization and robustness of metric learning algorithms. We first show
that, the adversarial margin, defined as the distance between training
instances and their closest adversarial examples in the input space, takes
account of both the distance margin in the feature space and the correlation
between the metric and triplet constraints. Next, to enhance robustness to
instance perturbation, we propose to enlarge the adversarial margin through
minimizing a derived novel loss function termed the perturbation loss. The
proposed loss can be viewed as a data-dependent regularizer and easily plugged
into any existing metric learning methods. Finally, we show that the enlarged
margin is beneficial to the generalization ability by using the theoretical
technique of algorithmic robustness. Experimental results on 16 datasets
demonstrate the superiority of the proposed method over existing
state-of-the-art methods in both discrimination accuracy and robustness against
possible noise.
