Distance metric learning (DML) has been studied extensively in the past
decades for its superior performance with distance-based algorithms. Most of
the existing methods propose to learn a distance metric with pairwise or
triplet constraints. However, the number of constraints is quadratic or even
cubic in the number of the original examples, which makes it challenging for
DML to handle the large-scale data set. Besides, the real-world data may
contain various uncertainty, especially for the image data. The uncertainty can
mislead the learning procedure and cause the performance degradation. By
investigating the image data, we find that the original data can be observed
from a small set of clean latent examples with different distortions. In this
work, we propose the margin preserving metric learning framework to learn the
distance metric and latent examples simultaneously. By leveraging the ideal
properties of latent examples, the training efficiency can be improved
significantly while the learned metric also becomes robust to the uncertainty
in the original data. Furthermore, we can show that the metric is learned from
latent examples only, but it can preserve the large margin property even for
the original data. The empirical study on the benchmark image data sets
demonstrates the efficacy and efficiency of the proposed method.

本文提出了一种保持边界的度量学习框架，同时学习距离度量和潜在样本。该方法在处理大规模数据集时具有高效性，并且可以使学习的度量对数据不确定性具有鲁棒性，并且通过实验证明了该方法的有效性和高效性。