Lorenzo Torresani, Kuang-chih Lee
Metric learning has been shown to signiﬁcantly improve the accuracy of k-nearest neighbor (kNN) classiﬁcation. In problems involving thousands of features, dis- tance learning algorithms cannot be used due to overﬁtting and high computa- tional complexity. In such cases, previous work has relied on a two-step solution: ﬁrst apply dimensionality reduction methods to the data, and then learn a met- ric in the resulting low-dimensional subspace. In this paper we show that better classiﬁcation performance can be achieved by unifying the objectives of dimen- sionality reduction and metric learning. We propose a method that solves for the low-dimensional projection of the inputs, which minimizes a metric objective aimed at separating points in different classes by a large margin. This projection is deﬁned by a signiﬁcantly smaller number of parameters than metrics learned in input space, and thus our optimization reduces the risks of overﬁtting. Theory and results are presented for both a linear as well as a kernelized version of the algorithm. Overall, we achieve classiﬁcation rates similar, and in several cases superior, to those of support vector machines.