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

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 cannotlinks. 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.