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Information-theoretic Metric Learning


Conference Paper


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

Links: PDF


  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}