Distance Metric Learning with Eigenvalue Optimization
Copyright © 2012 Yiming Ying and Peng Li. 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 eigenval...
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ftunivexeter:oai:ore.exeter.ac.uk:10871/11881 2023-05-15T16:01:39+02:00 Distance Metric Learning with Eigenvalue Optimization Ying, Yiming Peng, Li 2012 http://hdl.handle.net/10871/11881 en eng Microtome Publishing http://jmlr.org/papers/v13/ying12a.html Vol. 13, pp. 1 - 26 http://hdl.handle.net/10871/11881 1532-4435 1533-7928 Journal of Machine Learning Research metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization matrix factorization face verification Article 2012 ftunivexeter 2023-03-03T00:04:12Z Copyright © 2012 Yiming Ying and Peng Li. 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). Article in Journal/Newspaper DML University of Exeter: Open Research Exeter (ORE) |
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University of Exeter: Open Research Exeter (ORE) |
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ftunivexeter |
language |
English |
topic |
metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization matrix factorization face verification |
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metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization matrix factorization face verification Ying, Yiming Peng, Li Distance Metric Learning with Eigenvalue Optimization |
topic_facet |
metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization matrix factorization face verification |
description |
Copyright © 2012 Yiming Ying and Peng Li. 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). |
format |
Article in Journal/Newspaper |
author |
Ying, Yiming Peng, Li |
author_facet |
Ying, Yiming Peng, Li |
author_sort |
Ying, Yiming |
title |
Distance Metric Learning with Eigenvalue Optimization |
title_short |
Distance Metric Learning with Eigenvalue Optimization |
title_full |
Distance Metric Learning with Eigenvalue Optimization |
title_fullStr |
Distance Metric Learning with Eigenvalue Optimization |
title_full_unstemmed |
Distance Metric Learning with Eigenvalue Optimization |
title_sort |
distance metric learning with eigenvalue optimization |
publisher |
Microtome Publishing |
publishDate |
2012 |
url |
http://hdl.handle.net/10871/11881 |
genre |
DML |
genre_facet |
DML |
op_relation |
http://jmlr.org/papers/v13/ying12a.html Vol. 13, pp. 1 - 26 http://hdl.handle.net/10871/11881 1532-4435 1533-7928 Journal of Machine Learning Research |
_version_ |
1766397426298519552 |