Robust Metric Learning by Smooth Optimization
This work addresses noisy constraints in metric learning, which is incremental as it builds on existing methods by adding robustness to handle imperfections in side information.
The paper tackles the problem of learning distance metrics from noisy constraints, common in real-world applications like user feedback, by formulating it as a robust optimization problem and transforming it into convex programming. The proposed method uses smooth optimization with a worst-case convergence rate of O(1/√ε) and shows effectiveness on UCI datasets compared to state-of-the-art methods.
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.