Robust Metric Learning with Smooth Optimization

Kaizhu Huang, Rong Jin, Zenglin Xu, Cheng-Lin Liu
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:252-259, 2010.

Abstract

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’ im- plicit feedbacks and citations among arti- cles. As a result, these constraints are usu- ally noisy and contain many mistakes. In this work, we aim to learn a distance met- ric from noisy constraints by robust opti- mization 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 trans- formed 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/$\sqrt{}$$\varepsilon$) for smooth optimization problems, where $\varepsilon$ is the desired error of the approximate so- lution. Finally, our empirical study with UCI data sets demonstrate the effective- ness of the proposed method in comparison to state-of-the-art methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-huang10a, title = {Robust Metric Learning with Smooth Optimization}, author = {Huang, Kaizhu and Jin, Rong and Xu, Zenglin and Liu, Cheng-Lin}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {252--259}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/huang10a/huang10a.pdf}, url = {https://proceedings.mlr.press/r8/huang10a.html}, abstract = {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’ im- plicit feedbacks and citations among arti- cles. As a result, these constraints are usu- ally noisy and contain many mistakes. In this work, we aim to learn a distance met- ric from noisy constraints by robust opti- mization 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 trans- formed 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/$\sqrt{}$$\varepsilon$) for smooth optimization problems, where $\varepsilon$ is the desired error of the approximate so- lution. Finally, our empirical study with UCI data sets demonstrate the effective- ness of the proposed method in comparison to state-of-the-art methods.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Robust Metric Learning with Smooth Optimization %A Kaizhu Huang %A Rong Jin %A Zenglin Xu %A Cheng-Lin Liu %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-huang10a %I PMLR %P 252--259 %U https://proceedings.mlr.press/r8/huang10a.html %V R8 %X Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as users’ im- plicit feedbacks and citations among arti- cles. As a result, these constraints are usu- ally noisy and contain many mistakes. In this work, we aim to learn a distance met- ric from noisy constraints by robust opti- mization in a worst-case scenario, to which we refer as robust metric learning. We formulate the learning task initially as a combinatorial optimization problem, and show that it can be elegantly trans- formed to a convex programming problem. We present an efficient learning algorithm based on smooth optimization [7]. It has a worst-case convergence rate of O(1/$\sqrt{}$$\varepsilon$) for smooth optimization problems, where $\varepsilon$ is the desired error of the approximate so- lution. Finally, our empirical study with UCI data sets demonstrate the effective- ness of the proposed method in comparison to state-of-the-art methods. %Z Reissued by PMLR on 04 October 2026.
APA
Huang, K., Jin, R., Xu, Z. & Liu, C.. (2010). Robust Metric Learning with Smooth Optimization. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:252-259 Available from https://proceedings.mlr.press/r8/huang10a.html. Reissued by PMLR on 04 October 2026.

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