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# A metric learning perspective of SVM: on the relation of LMNN and SVM

*Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics*, PMLR 22:308-317, 2012.

#### Abstract

Support Vector Machines, SVMs, and the Large Margin Nearest Neighbor algorithm, LMNN, are two very popular learning algorithms with quite different learning biases. In this paper we bring them into a unified view and show that they have a much stronger relation than what is commonly thought. We analyze SVMs from a metric learning perspective and cast them as a metric learning problem, a view which helps us uncover the relations of the two algorithms. We show that LMNN can be seen as learning a set of local SVM-like models in a quadratic space. Along the way and inspired by the metric-based interpretation of SVMs we derive a novel variant of SVMs, ε-SVM, to which LMNN is even more similar. We give a unified view of LMNN and the different SVM variants. Finally we provide some preliminary experiments on a number of benchmark datasets in which show that ε-SVM compares favorably both with respect to LMNN and SVM.