Robust Distance Metric Learning via Simultaneous L1-Norm Minimization and Maximization

Hua Wang, Feiping Nie, Heng Huang

ICML - 2014

Traditional distance metric learning with side information usually formulates the objectives using the covariance matrices of the data point pairs in the two constraint sets of must-links and cannot-links. Because the covariance matrix computes the sum of the squared l2-norm distances, it is prone to both outlier samples and outlier features. To develop a robust distance metric learning method, we propose a new objective for distance metric learning using the l1-norm distances. The resulted objective is challenging to solve, because it simultaneously minimizes and maximizes (minmax) a number of non-smooth l1-norm terms. As an important theoretical contribution of this paper, we systematically derive an efficient iterative algorithm to solve the general l1-norm minmax problem. We performed extensive empirical evaluations, where our new distance metric learning method outperforms related state-of-the-art methods in a variety of experimental settings.


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Wang, Hua, Feiping Nie, and Heng Huang. "Robust distance metric learning via simultaneous l1-norm minimization and maximization." International conference on machine learning. 2014.
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  title={Robust distance metric learning via simultaneous l1-norm minimization and maximization},
  author={Wang, Hua and Nie, Feiping and Huang, Heng},
  booktitle={International conference on machine learning},