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Low-rank quadratic semidefinite programming
Low-rank quadratic semidefinite programming
Type
Article
Authors
Yuan, Ganzhao
Zhang, Zhenjie
Ghanem, Bernard
Hao, Zhifeng
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Visual Computing Center (VCC)
VCC Analytics Research Group
Date
2013-04
Abstract
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Citation
Yuan, G., Zhang, Z., Ghanem, B., & Hao, Z. (2013). Low-rank quadratic semidefinite programming. Neurocomputing, 106, 51–60. doi:10.1016/j.neucom.2012.10.014
Acknowledgements
Yuan and Hao are supported by NSF-China (61070033, 61100148), NSF-Guangdong (9251009001000005, S2011040004804), Key Technology Research and Development Programs of Guangdong Province (2010B050400011).
Publisher
Elsevier BV
Journal
Neurocomputing
DOI
10.1016/j.neucom.2012.10.014
Permanent link to this record
http://hdl.handle.net/10754/562701
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Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division
Electrical and Computer Engineering Program
Visual Computing Center (VCC)
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