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Information-theoretic Metric Learning

2006

Conference Paper

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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.

Author(s): Davis, J. and Kulis, B. and Sra, S. and Dhillon, I.
Journal: NIPS 2006 Workshop on Learning to Compare Examples
Pages: 1-5
Year: 2006
Month: December
Day: 0

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: NIPS 2006 Workshop on Learning to Compare Examples
Event Place: Whistler, BC, Canada

Digital: 0
Institution: Univ. of Texas, Austin
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5238,
  title = {Information-theoretic Metric Learning},
  author = {Davis, J. and Kulis, B. and Sra, S. and Dhillon, I.},
  journal = {NIPS 2006 Workshop on Learning to Compare Examples},
  pages = {1-5},
  organization = {Max-Planck-Gesellschaft},
  institution = {Univ. of Texas, Austin},
  school = {Biologische Kybernetik},
  month = dec,
  year = {2006},
  month_numeric = {12}
}