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Article: Consistency of sparse PCA in High Dimension, Low Sample Size contexts

TitleConsistency of sparse PCA in High Dimension, Low Sample Size contexts
Authors
KeywordsConsistency
High dimension
Low sample size
Sparse PCA
Issue Date2013
Citation
Journal of Multivariate Analysis, 2013, v. 115, p. 317-333 How to Cite?
AbstractSparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension, Low Sample Size (HDLSS)). We consider the previously studied single spike covariance model and assume in addition that the maximal eigenvector is sparse. We extend the existing HDLSS asymptotic consistency and strong inconsistency results of conventional PCA in an entirely new direction. We find a large set of sparsity assumptions under which sparse PCA is still consistent even when conventional PCA is strongly inconsistent. The consistency of sparse PCA is characterized along with rates of convergence. Furthermore, we clearly identify the mathematical boundaries of the sparse PCA consistency, by showing strong inconsistency for an oracle version of sparse PCA beyond the consistent region, as well as its inconsistency on the boundaries of the consistent region. Simulation studies are performed to validate the asymptotic results in finite samples. © 2012 Elsevier Inc.
Persistent Identifierhttp://hdl.handle.net/10722/219681
ISSN
2015 Impact Factor: 0.857
2015 SCImago Journal Rankings: 1.458

 

DC FieldValueLanguage
dc.contributor.authorShen, Dan-
dc.contributor.authorShen, Haipeng-
dc.contributor.authorMarron, J. S.-
dc.date.accessioned2015-09-23T02:57:42Z-
dc.date.available2015-09-23T02:57:42Z-
dc.date.issued2013-
dc.identifier.citationJournal of Multivariate Analysis, 2013, v. 115, p. 317-333-
dc.identifier.issn0047-259X-
dc.identifier.urihttp://hdl.handle.net/10722/219681-
dc.description.abstractSparse Principal Component Analysis (PCA) methods are efficient tools to reduce the dimension (or number of variables) of complex data. Sparse principal components (PCs) are easier to interpret than conventional PCs, because most loadings are zero. We study the asymptotic properties of these sparse PC directions for scenarios with fixed sample size and increasing dimension (i.e. High Dimension, Low Sample Size (HDLSS)). We consider the previously studied single spike covariance model and assume in addition that the maximal eigenvector is sparse. We extend the existing HDLSS asymptotic consistency and strong inconsistency results of conventional PCA in an entirely new direction. We find a large set of sparsity assumptions under which sparse PCA is still consistent even when conventional PCA is strongly inconsistent. The consistency of sparse PCA is characterized along with rates of convergence. Furthermore, we clearly identify the mathematical boundaries of the sparse PCA consistency, by showing strong inconsistency for an oracle version of sparse PCA beyond the consistent region, as well as its inconsistency on the boundaries of the consistent region. Simulation studies are performed to validate the asymptotic results in finite samples. © 2012 Elsevier Inc.-
dc.languageeng-
dc.relation.ispartofJournal of Multivariate Analysis-
dc.subjectConsistency-
dc.subjectHigh dimension-
dc.subjectLow sample size-
dc.subjectSparse PCA-
dc.titleConsistency of sparse PCA in High Dimension, Low Sample Size contexts-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jmva.2012.10.007-
dc.identifier.scopuseid_2-s2.0-84869784137-
dc.identifier.volume115-
dc.identifier.spage317-
dc.identifier.epage333-
dc.identifier.eissn1095-7243-

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