Most existing distance metric learning methods assume perfect side
information that is usually given in pairwise or triplet constraints. Instead,
in many real-world applications, the constraints are derived from side
information, such as users' implicit feedbacks and citations among articles. As
a result, these constraints are usually noisy and contain many mistakes. In
this work, we aim to learn a distance metric from noisy constraints by robust
optimization in a worst-case scenario, to which we refer as robust metric
learning. We formulate the learning task initially as a combinatorial
optimization problem, and show that it can be elegantly transformed to a convex
programming problem. We present an efficient learning algorithm based on smooth
optimization [7]. It has a worst-case convergence rate of
O(1/{\surd}{\varepsilon}) for smooth optimization problems, where {\varepsilon}
is the desired error of the approximate solution. Finally, our empirical study
with UCI data sets demonstrate the effectiveness of the proposed method in
comparison to state-of-the-art methods.

本文提出了一种称为鲁棒测度学习的方法，旨在从嘈杂的侧面信息中学习距离度量，将学习任务最初制定为组合优化问题，并将其优雅地转换为凸规划问题，提出了一种基于平滑优化的高效学习算法，最后在 UCI 数据集上的实验研究证明了所提出方法的有效性。