Information-theoretic metric learning

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Information-theoretic metric learning (2007)

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by Jason Davis , Brian Kulis , Suvrit Sra , Inderjit Dhillon

Venue:	in NIPS 2006 Workshop on Learning to Compare Examples
Citations:	359 - 15 self

BibTeX

@INPROCEEDINGS{Davis07information-theoreticmetric,
    author = {Jason Davis and Brian Kulis and Suvrit Sra and Inderjit Dhillon},
    title = {Information-theoretic metric learning},
    booktitle = {in NIPS 2006 Workshop on Learning to Compare Examples},
    year = {2007}
}

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Abstract

We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a low-rank kernel learning problem. Specifically, we minimize the Burg divergence of a low-rank kernel to an input kernel, subject to pairwise distance constraints. Our approach has several advantages over existing methods. First, we present a natural information-theoretic formulation for the problem. Second, the algorithm utilizes the methods developed by Kulis et al. [6], which do not involve any eigenvector computation; in particular, the running time of our method is faster than most existing techniques. Third, the formulation offers insights into connections between metric learning and kernel learning. 1

Keyphrases

information-theoretic metric learning kernel learning surprising equivalence differential relative entropy low-rank kernel learning problem natural information-theoretic formulation burg divergence low-rank kernel input kernel metric learning problem metric learning multivariate gaussians running time distance constraint several advantage eigenvector computation mahalanobis distance function

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