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Article: The analysis of two-way functional data using two-way regularized singular value decompositions

TitleThe analysis of two-way functional data using two-way regularized singular value decompositions
Authors
KeywordsFunctional data analysis
Penalization
Regularization
Spatial-temporal modeling
Basis expansion
Issue Date2009
Citation
Journal of the American Statistical Association, 2009, v. 104, n. 488, p. 1609-1620 How to Cite?
AbstractTwo-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from oneway regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross- validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several "natural" approaches to penalized SVDs are flawed and explain why so. © 2009 American Statistical Association.
Persistent Identifierhttp://hdl.handle.net/10722/219613
ISSN
2015 Impact Factor: 1.725
2015 SCImago Journal Rankings: 3.447

 

DC FieldValueLanguage
dc.contributor.authorHuang, Jianhua Z.-
dc.contributor.authorShen., Haipeng-
dc.contributor.authorBuja., Andreas-
dc.date.accessioned2015-09-23T02:57:31Z-
dc.date.available2015-09-23T02:57:31Z-
dc.date.issued2009-
dc.identifier.citationJournal of the American Statistical Association, 2009, v. 104, n. 488, p. 1609-1620-
dc.identifier.issn0162-1459-
dc.identifier.urihttp://hdl.handle.net/10722/219613-
dc.description.abstractTwo-way functional data consist of a data matrix whose row and column domains are both structured, for example, temporally or spatially, as when the data are time series collected at different locations in space. We extend one-way functional principal component analysis (PCA) to two-way functional data by introducing regularization of both left and right singular vectors in the singular value decomposition (SVD) of the data matrix. We focus on a penalization approach and solve the nontrivial problem of constructing proper two-way penalties from oneway regression penalties. We introduce conditional cross-validated smoothing parameter selection whereby left-singular vectors are cross- validated conditional on right-singular vectors, and vice versa. The concept can be realized as part of an alternating optimization algorithm. In addition to the penalization approach, we briefly consider two-way regularization with basis expansion. The proposed methods are illustrated with one simulated and two real data examples. Supplemental materials available online show that several "natural" approaches to penalized SVDs are flawed and explain why so. © 2009 American Statistical Association.-
dc.languageeng-
dc.relation.ispartofJournal of the American Statistical Association-
dc.subjectFunctional data analysis-
dc.subjectPenalization-
dc.subjectRegularization-
dc.subjectSpatial-temporal modeling-
dc.subjectBasis expansion-
dc.titleThe analysis of two-way functional data using two-way regularized singular value decompositions-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1198/jasa.2009.tm08024-
dc.identifier.scopuseid_2-s2.0-74049162796-
dc.identifier.volume104-
dc.identifier.issue488-
dc.identifier.spage1609-
dc.identifier.epage1620-

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