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Distance metric learning with eigenvalue optimization (2012)
| Venue: | Journal of Machine Learning Research (Special Topics on Kernel and Metric Learning |
| Citations: | 45 - 1 self |
BibTeX
@INPROCEEDINGS{Ying12distancemetric,
author = {Yiming Ying and Peng Li and Sören Sonnenburg and Francis Bach and Cheng Soon Ong},
title = {Distance metric learning with eigenvalue optimization},
booktitle = {Journal of Machine Learning Research (Special Topics on Kernel and Metric Learning},
year = {2012},
pages = {1--26}
}
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Abstract
The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, we formulate LMNN (Weinberger et al., 2005), one of the state-of-the-art metric learning methods, as a similar eigenvalue optimization problem. This novel framework not only provides new insights into metric learning but also opens new avenues to the design of efficient metric learning algorithms. Indeed, first-order algorithms are developed for DML-eig and LMNN which only need the computation of the largest eigenvector of a matrix per iteration. Their convergence characteristics are rigorously established. Various experiments on benchmark data sets show the competitive performance of our new approaches. In addition, we report an encouraging result on a difficult and challenging face verification data set called Labeled Faces in the Wild (LFW).
Keyphrases
eigenvalue optimization new insight challenging face verification data encouraging result symmetric matrix novel framework novel metric learning approach first-order algorithm convergence characteristic new avenue benchmark data set labeled face competitive performance new approach well-known eigenvalue optimization problem similar eigenvalue optimization problem novel eigenvalue optimization framework main theme various experiment maximal eigenvalue metric learning
