Low-rank quadratic semidefinite programming

Handle URI:
http://hdl.handle.net/10754/562701
Title:
Low-rank quadratic semidefinite programming
Authors:
Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard ( 0000-0002-5534-587X ) ; Hao, Zhifeng
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Electrical Engineering Program; Visual Computing Center (VCC); VCC Analytics Research Group
Publisher:
Elsevier
Journal:
Neurocomputing
Issue Date:
Apr-2013
DOI:
10.1016/j.neucom.2012.10.014
Type:
Article
ISSN:
09252312
Sponsors:
Yuan and Hao are supported by NSF-China (61070033, 61100148), NSF-Guangdong (9251009001000005, S2011040004804), Key Technology Research and Development Programs of Guangdong Province (2010B050400011).
Appears in Collections:
Articles; Electrical Engineering Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorYuan, Ganzhaoen
dc.contributor.authorZhang, Zhenjieen
dc.contributor.authorGhanem, Bernarden
dc.contributor.authorHao, Zhifengen
dc.date.accessioned2015-08-03T11:02:08Zen
dc.date.available2015-08-03T11:02:08Zen
dc.date.issued2013-04en
dc.identifier.issn09252312en
dc.identifier.doi10.1016/j.neucom.2012.10.014en
dc.identifier.urihttp://hdl.handle.net/10754/562701en
dc.description.abstractLow 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.en
dc.description.sponsorshipYuan and Hao are supported by NSF-China (61070033, 61100148), NSF-Guangdong (9251009001000005, S2011040004804), Key Technology Research and Development Programs of Guangdong Province (2010B050400011).en
dc.publisherElsevieren
dc.subjectEigenvalue decompositionen
dc.subjectKernel learningen
dc.subjectLow-rank and sparse matrix approximationen
dc.subjectMetric learningen
dc.subjectSemidefinite programmingen
dc.titleLow-rank quadratic semidefinite programmingen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentElectrical Engineering Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentVCC Analytics Research Groupen
dc.identifier.journalNeurocomputingen
dc.contributor.institutionSchool of Computer Science and Engineering, South China University of Technology, Chinaen
dc.contributor.institutionAdvanced Digital Sciences Center, Illinois at Singapore Pte, Singaporeen
dc.contributor.institutionFaculty of Computer, Guangdong University of Technology, Chinaen
kaust.authorGhanem, Bernarden
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