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dc.contributor.authorXu, Lijun
Yu, Bo
Zhang, Yin
dc.date.accessioned 2017-11-14T18:08:24Z
dc.date.available 2017-11-14T18:08:24Z
dc.date.issued 2017
dc.identifier.citation Xu, Lijun, Yu, Bo and Zhang, Yin. "An alternating direction and projection algorithm for structure-enforced matrix factorization." Computational Optimization and Applications, 68, no. 2 (2017) Springer: 333-362. https://doi.org/10.1007/s10589-017-9913-x.
dc.identifier.urihttps://hdl.handle.net/1911/98812
dc.description.abstract Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.
dc.language.iso eng
dc.publisher Springer
dc.rights This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer.
dc.title An alternating direction and projection algorithm for structure-enforced matrix factorization
dc.type Journal article
dc.citation.journalTitle Computational Optimization and Applications
dc.subject.keywordMatrix Factorization
Alternating Direction Method
Projection
Adaptive Penalty Parameter
Sparse Optimization
Dictionary Learning
dc.citation.volumeNumber 68
dc.citation.issueNumber 2
dc.identifier.digital revised_SeMF
dc.type.dcmi Text
dc.identifier.doihttps://doi.org/10.1007/s10589-017-9913-x
dc.type.publication post-print
dc.citation.firstpage 333
dc.citation.lastpage 362


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