Robust Metric Learning by Smooth Optimization
Kaizhu Huang, Rong Jin, Zenglin Xu, Cheng-Lin Liu
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 . It has a worst-case convergence rate of O(1/√ε) for smooth optimization problems, where ε 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.
PDF Link: /papers/10/p244-huang.pdf
AUTHOR = "Kaizhu Huang
and Rong Jin and Zenglin Xu and Cheng-Lin Liu",
TITLE = "Robust Metric Learning by Smooth Optimization",
BOOKTITLE = "Proceedings of the Twenty-Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-10)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2010",
PAGES = "244--251"