Fast Solvers and Efficient Implementations for Distance Metric Learning

author: Kilian Q. Weinberger, Department of Computer Science, Cornell University
published: Aug. 5, 2008,   recorded: July 2008,   views: 9072


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In this paper we study how to improve nearest neighbor classification by learning a Mahalanobis distance metric. We build on a recently proposed framework for distance metric learning known as large margin nearest neighbor (LMNN) classification. Within this framework, we focus specifically on the challenges in scalability and adaptability posed by large data sets. Our paper makes three contributions. First, we describe a highly efficient solver for the particular instance of semidefinite programming that arises in LMNN classification; our solver can handle problems with billions of large margin constraints in a few hours. Second, we show how to reduce both training and testing times using metric ball trees; the speedups from ball trees are further magnified by learning low dimensional representations of the input space. Third, we show how to learn different Mahalanobis distance metrics in different parts of the input space. For large data sets, these mixtures of locally adaptive metrics lead to even lower error rates.

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