Robust Semi-Supervised Metric Learning Meets with High Dimensionality
Abstract: Classical semi-supervised metric learning usually formulates the objectives via maximizing/minimizing the ratio formed with must-links and cannot-links. However, the presence of noise and adversarial attacks can result in incorrect pairings, which will diminish the reliability of learned projection directions. To develop a robust distance metric learning method, we propose a new objective for distance metric learning using the $\ell_{2,q}$-norm ($0<q<2$) distances which will alleviate the influence of outliers or adversarial attacks. We develop an algorithm that will decrease the objective monotonically with updates. Additionally, we address computational burdens (e.g., $\mathcal{O}(d^3)$ complexity, where $d$ is the size of features) by introducing a 2D metric learning algorithm and extending it to arbitrary dimensions with kernel methods, backed by theoretical guarantees. Extensive empirical evaluations consistently demonstrate the superiority of our methods across various experimental setups.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Cho-Jui_Hsieh1
Submission Number: 2360
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