Fast solvers and efficient implementations for distance metric learning

Fast solvers and efficient implementations for distance metric learning (2008)

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by Kilian Q. Weinberger , Lawrence K. Saul

Venue:	In ICML
Citations:	85 - 7 self

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@INPROCEEDINGS{Weinberger08fastsolvers,
    author = {Kilian Q. Weinberger and Lawrence K. Saul},
    title = {Fast solvers and efficient implementations for distance metric learning},
    booktitle = {In ICML},
    year = {2008}
}

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Abstract

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. 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, the use of locally adaptive distance metrics leads to even lower error rates. 1.

Keyphrases

efficient implementation distance metric learning fast solver input space semidefinite programming metric ball tree different mahalanobis distance metric particular instance mahalanobis distance large margin constraint large data set lmnn classification large margin neighbor classification different part adaptive distance metric ball tree low dimensional representation error rate efficient solver