Distance metric learning with eigenvalue optimization
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...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.413.7512 2023-05-15T16:01:38+02:00 Distance metric learning with eigenvalue optimization Yiming Ying Peng Li Sören Sonnenburg Francis Bach Cheng Soon Ong The Pennsylvania State University CiteSeerX Archives 2012 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7512 http://jmlr.org/papers/volume13/ying12a/ying12a.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7512 http://jmlr.org/papers/volume13/ying12a/ying12a.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://jmlr.org/papers/volume13/ying12a/ying12a.pdf metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization text 2012 ftciteseerx 2016-01-08T03:29:38Z 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). Text DML Unknown |
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metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization |
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metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization Yiming Ying Peng Li Sören Sonnenburg Francis Bach Cheng Soon Ong Distance metric learning with eigenvalue optimization |
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metric learning convex optimization semi-definite programming first-order methods eigenvalue optimization |
description |
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). |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Yiming Ying Peng Li Sören Sonnenburg Francis Bach Cheng Soon Ong |
author_facet |
Yiming Ying Peng Li Sören Sonnenburg Francis Bach Cheng Soon Ong |
author_sort |
Yiming Ying |
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 |
publishDate |
2012 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7512 http://jmlr.org/papers/volume13/ying12a/ying12a.pdf |
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DML |
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DML |
op_source |
http://jmlr.org/papers/volume13/ying12a/ying12a.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.7512 http://jmlr.org/papers/volume13/ying12a/ying12a.pdf |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766397404340289536 |