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Article: Sparse principal component analysis via regularized low rank matrix approximation

TitleSparse principal component analysis via regularized low rank matrix approximation
Authors
KeywordsDimension reduction
High-dimension-low-sample-size
Regularization
Thresholding
Singular value decomposition
Issue Date2008
Citation
Journal of Multivariate Analysis, 2008, v. 99, n. 6, p. 1015-1034 How to Cite?
AbstractPrincipal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loadings with very few non-zero elements. In this paper, we propose a new sparse PCA method, namely sparse PCA via regularized SVD (sPCA-rSVD). We use the connection of PCA with singular value decomposition (SVD) of the data matrix and extract the PCs through solving a low rank matrix approximation problem. Regularization penalties are introduced to the corresponding minimization problem to promote sparsity in PC loadings. An efficient iterative algorithm is proposed for computation. Two tuning parameter selection methods are discussed. Some theoretical results are established to justify the use of sPCA-rSVD when only the data covariance matrix is available. In addition, we give a modified definition of variance explained by the sparse PCs. The sPCA-rSVD provides a uniform treatment of both classical multivariate data and high-dimension-low-sample-size (HDLSS) data. Further understanding of sPCA-rSVD and some existing alternatives is gained through simulation studies and real data examples, which suggests that sPCA-rSVD provides competitive results. © 2007 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/219568
ISSN
2015 Impact Factor: 0.857
2015 SCImago Journal Rankings: 1.458

 

DC FieldValueLanguage
dc.contributor.authorShen, Haipeng-
dc.contributor.authorHuang, Jianhua Z.-
dc.date.accessioned2015-09-23T02:57:25Z-
dc.date.available2015-09-23T02:57:25Z-
dc.date.issued2008-
dc.identifier.citationJournal of Multivariate Analysis, 2008, v. 99, n. 6, p. 1015-1034-
dc.identifier.issn0047-259X-
dc.identifier.urihttp://hdl.handle.net/10722/219568-
dc.description.abstractPrincipal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loadings with very few non-zero elements. In this paper, we propose a new sparse PCA method, namely sparse PCA via regularized SVD (sPCA-rSVD). We use the connection of PCA with singular value decomposition (SVD) of the data matrix and extract the PCs through solving a low rank matrix approximation problem. Regularization penalties are introduced to the corresponding minimization problem to promote sparsity in PC loadings. An efficient iterative algorithm is proposed for computation. Two tuning parameter selection methods are discussed. Some theoretical results are established to justify the use of sPCA-rSVD when only the data covariance matrix is available. In addition, we give a modified definition of variance explained by the sparse PCs. The sPCA-rSVD provides a uniform treatment of both classical multivariate data and high-dimension-low-sample-size (HDLSS) data. Further understanding of sPCA-rSVD and some existing alternatives is gained through simulation studies and real data examples, which suggests that sPCA-rSVD provides competitive results. © 2007 Elsevier Inc. All rights reserved.-
dc.languageeng-
dc.relation.ispartofJournal of Multivariate Analysis-
dc.subjectDimension reduction-
dc.subjectHigh-dimension-low-sample-size-
dc.subjectRegularization-
dc.subjectThresholding-
dc.subjectSingular value decomposition-
dc.titleSparse principal component analysis via regularized low rank matrix approximation-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jmva.2007.06.007-
dc.identifier.scopuseid_2-s2.0-43049086717-
dc.identifier.volume99-
dc.identifier.issue6-
dc.identifier.spage1015-
dc.identifier.epage1034-
dc.identifier.eissn1095-7243-

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