While distance function learning for supervised learning tasks has a long history, extending it to learning tasks with weaker supervisory information has only been studied recently. In particular, some methods have been proposed for semi-supervised metric learning based on pairwise similarity or dissimilarity information. In this paper, we propose a kernel approach for semi-supervised metric learning and present in detail two special cases of this kernel approach. The metric learning problem is

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... thus formulated as an optimization problem for kernel learning. An attractive property of the optimization problem is that it is convex and hence has no local optima. While a closed-form solution exists for the first special case, the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically. Experimental results based on both synthetic and real-world data show that this new kernel approach is promising for nonlinear metric learning. Index Terms-metric learning, kernel learning, semisupervised learning, clustering.