Learning a Distance Metric by Empirical Loss Minimization

Bian, Wei; Tao, Dacheng

doi:10.5591/978-1-57735-516-8/IJCAI11-202

Learning a Distance Metric by Empirical Loss Minimization

Wei Bian, Dacheng Tao

Download BibTeX Cite

Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence. Pages 1186-1190.

https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-202

Abstract

In this paper, we study the problem of learning ametric and propose a loss function based metriclearning framework, in which the metric is estimatedby minimizing an empirical risk over a trainingset. With mild conditions on the instance distributionand the used loss function, we prove that theempirical risk converges to its expected counterpartat rate O(1/sqrt{n}), wherein n is the cardinality of the training set. In addition, with the assumption thatthe best metric that minimizes the expected risk isbounded, we prove that the learned metric is consistent. Two example algorithms are presented by usingthe proposed loss function based metric learningframework, each of which uses a log loss functionand a smoothed hinge loss function, respectively. Experimental results on data sets from the UCI machine learning repository suggest the effectivenessof the proposed algorithms.

Wei Bian, and Dacheng Tao. 2011. Learning a Distance Metric by Empirical Loss Minimization. In Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11. IJCAI, 1186–1190. https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-202

@inproceedings{ijcai2011p202,
  title     = {Learning a Distance Metric by Empirical Loss Minimization},
  author    = {Bian, Wei and Tao, Dacheng},
  booktitle = {Proceedings of the Twenty-Second International Joint Conference on
               Artificial Intelligence, {IJCAI-11}},
  publisher = {AAAI Press/International Joint Conferences on Artificial Intelligence},
  editor    = {Toby Walsh},
  pages     = {1186--1190},
  year      = {2011},
  month     = {7},
  doi       = {10.5591/978-1-57735-516-8/IJCAI11-202},
  url       = {https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-202},
}

TY  - CPAPER
TI  - Learning a Distance Metric by Empirical Loss Minimization
AU  - Bian, Wei
AU  - Tao, Dacheng
T2  - Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, IJCAI-11
PB  - AAAI Press/International Joint Conferences on Artificial Intelligence
PY  - 2011
SP  - 1186
EP  - 1190
DO  - 10.5591/978-1-57735-516-8/IJCAI11-202
UR  - https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-202
ER  -