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Conference Paper

Information-theoretic Metric Learning


Kulis B, Sra,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Davis, J., Kulis B, Sra, S., & Dhillon, I. (2006). Information-theoretic Metric Learning. In NIPS 2006 Workshop on Learning to Compare Examples (pp. 1-5).

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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.