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Information-theoretic Metric Learning

2007

Conference Paper

ei


In this paper, we present an information-theoretic approach to learning a Mahalanobis distance function. We formulate the problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the distance function. We express this problem as a particular Bregman optimization problem---that of minimizing the LogDet divergence subject to linear constraints. Our resulting algorithm has several advantages over existing methods. First, our method can handle a wide variety of constraints and can optionally incorporate a prior on the distance function. Second, it is fast and scalable. Unlike most existing methods, no eigenvalue computations or semi-definite programming are required. We also present an online version and derive regret bounds for the resulting algorithm. Finally, we evaluate our method on a recent error reporting system for software called Clarify, in the context of metric learning for nearest neighbor classification, as well as on standard data sets.

Author(s): Davis, JV. and Kulis, B. and Jain, P. and Sra, S. and Dhillon, IS.
Book Title: ICML 2007
Journal: Proceedings of the 24th Annual International Conference on Machine Learning (ICML 2007)
Pages: 209-216
Year: 2007
Month: June
Day: 0
Editors: Ghahramani, Z.
Publisher: ACM Press

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

DOI: 10.1145/1273496.1273523
Event Name: 24th Annual International Conference on Machine Learning
Event Place: Corvallis, OR, USA

Address: New York, NY, USA
Digital: 0
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

Links: Web

BibTex

@inproceedings{5127,
  title = {Information-theoretic Metric Learning},
  author = {Davis, JV. and Kulis, B. and Jain, P. and Sra, S. and Dhillon, IS.},
  journal = {Proceedings of the 24th Annual International Conference on Machine Learning (ICML 2007)},
  booktitle = {ICML 2007},
  pages = {209-216},
  editors = {Ghahramani, Z. },
  publisher = {ACM Press},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {New York, NY, USA},
  month = jun,
  year = {2007},
  month_numeric = {6}
}