Backward-forward least angle shrinkage for sparse quadratic optimization

Zhou, T; Tao, D

Backward-forward least angle shrinkage for sparse quadratic optimization

Zhou, T Tao, D

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Publication Type:: Conference Proceeding
Citation:: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2010, 6443 LNCS (PART 1), pp. 388 - 396
Issue Date:: 2010-12-21

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Field	Value	Language
dc.contributor.author	Zhou, T	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.date.issued	2010-12-21	en_US
dc.identifier.citation	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2010, 6443 LNCS (PART 1), pp. 388 - 396	en_US
dc.identifier.isbn	3642175368	en_US
dc.identifier.isbn	9783642175367	en_US
dc.identifier.issn	0302-9743	en_US
dc.identifier.uri	http://hdl.handle.net/10453/16146
dc.description.abstract	In compressed sensing and statistical society, dozens of algorithms have been developed to solve ℓ1 penalized least square regression, but constrained sparse quadratic optimization (SQO) is still an open problem. In this paper, we propose backward-forward least angle shrinkage (BF-LAS), which provides a scheme to solve general SQO including sparse eigenvalue minimization. BF-LAS starts from the dense solution, iteratively shrinks unimportant variables' magnitudes to zeros in the backward step for minimizing the ℓ1 norm, decreases important variables' gradients in the forward step for optimizing the objective, and projects the solution on the feasible set defined by the constraints. The importance of a variable is measured by its correlation w.r.t the objective and is updated via least angle shrinkage (LAS). We show promising performance of BF-LAS on sparse dimension reduction. © 2010 Springer-Verlag.	en_US
dc.relation.ispartof	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en_US
dc.relation.isbasedon	10.1007/978-3-642-17537-4_48	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Backward-forward least angle shrinkage for sparse quadratic optimization	en_US
dc.type	Conference Proceeding
utslib.citation.volume	PART 1	en_US
utslib.citation.volume	6443 LNCS	en_US
utslib.for	080108 Neural, Evolutionary and Fuzzy Computation	en_US
dc.location.activity	Sydney, Australia	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.issue	PART 1	en_US
pubs.publication-status	Published	en_US
pubs.volume	6443 LNCS	en_US

Abstract:

In compressed sensing and statistical society, dozens of algorithms have been developed to solve ℓ1 penalized least square regression, but constrained sparse quadratic optimization (SQO) is still an open problem. In this paper, we propose backward-forward least angle shrinkage (BF-LAS), which provides a scheme to solve general SQO including sparse eigenvalue minimization. BF-LAS starts from the dense solution, iteratively shrinks unimportant variables' magnitudes to zeros in the backward step for minimizing the ℓ1 norm, decreases important variables' gradients in the forward step for optimizing the objective, and projects the solution on the feasible set defined by the constraints. The importance of a variable is measured by its correlation w.r.t the objective and is updated via least angle shrinkage (LAS). We show promising performance of BF-LAS on sparse dimension reduction. © 2010 Springer-Verlag.

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http://hdl.handle.net/10453/16146