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Type: Conference paper
Title: A scalable dual approach to semidefinite metric learning
Author: Shen, C.
Kim, J.
Wang, L.
Citation: Proceedings of the 2011 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 11): pp.2601-2608
Publisher: IEEE
Publisher Place: USA
Issue Date: 2011
Series/Report no.: IEEE Conference on Computer Vision and Pattern Recognition
ISBN: 9781457703942
ISSN: 1063-6919
Conference Name: IEEE Conference on Computer Vision and Pattern Recognition (24th : 2011 : Colorado Springs, CO, U.S.A.)
Statement of
Chunhua Shen, Junae Kim and Lei Wang
Abstract: Distance metric learning plays an important role in many vision problems. Previous work of quadratic Maha-lanobis metric learning usually needs to solve a semidef- inite programming (SDP) problem. A standard interior-point SDP solver has a complexity of O((D6.5)(with D the dimension of input data), and can only solve problems up to a few thousand variables. Since the number of vari- ables is D(D + 1)/2, this corresponds to a limit around D < 100. This high complexity hampers the application of metric learning to high-dimensional problems. In this work, we propose a very efficient approach to this metric learning problem. We formulate a Lagrange dual approach which is much simpler to optimize, and we can solve much larger Mahalanobismetric learning problems. Roughly, the proposed approach has a time complexity of O(t •D3) with t _ 20 _ 30 for most problems in our experiments. The proposed algorithm is scalable and easy to implement. Ex- periments on various datasets show its similar accuracy compared with state-of-the-art. We also demonstrate that this idea may also be able to be applied to other SDP problems such as maximum variance unfolding.
Rights: Copyright status unknown
DOI: 10.1109/CVPR.2011.5995447
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