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Article: Singular value decomposition and its visualization
Title | Singular value decomposition and its visualization |
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Authors | |
Keywords | Functional data analysis Exploratory data analysis Principal component analysis |
Issue Date | 2007 |
Citation | Journal of Computational and Graphical Statistics, 2007, v. 16, n. 4, p. 833-854 How to Cite? |
Abstract | Singular value decomposition (SVD) is a useful tool in functional data analysis (FDA). Compared to principal component analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed to select an appropriate centering in practice. Several useful matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, image plots, curve movies, and rotation movies. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, show local variations, and highlight interactions between columns and rows. Several toy examples are designed to compare the different variations of SVD, and real data examples are used to illustrate the usefulness of the visualization methods. © 2007 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. |
Persistent Identifier | http://hdl.handle.net/10722/219552 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 1.530 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Zhang, Lingsong | - |
dc.contributor.author | Marron, J. S. | - |
dc.contributor.author | Shen, Haipeng | - |
dc.contributor.author | Zhu, Zhengyuan | - |
dc.date.accessioned | 2015-09-23T02:57:23Z | - |
dc.date.available | 2015-09-23T02:57:23Z | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | Journal of Computational and Graphical Statistics, 2007, v. 16, n. 4, p. 833-854 | - |
dc.identifier.issn | 1061-8600 | - |
dc.identifier.uri | http://hdl.handle.net/10722/219552 | - |
dc.description.abstract | Singular value decomposition (SVD) is a useful tool in functional data analysis (FDA). Compared to principal component analysis (PCA), SVD is more fundamental, because SVD simultaneously provides the PCAs in both row and column spaces. We compare SVD and PCA from the FDA view point, and extend the usual SVD to variations by considering different centerings. A generalized scree plot is proposed to select an appropriate centering in practice. Several useful matrix views of the SVD components are introduced to explore different features in data, including SVD surface plots, image plots, curve movies, and rotation movies. These methods visualize both column and row information of a two-way matrix simultaneously, relate the matrix to relevant curves, show local variations, and highlight interactions between columns and rows. Several toy examples are designed to compare the different variations of SVD, and real data examples are used to illustrate the usefulness of the visualization methods. © 2007 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Computational and Graphical Statistics | - |
dc.subject | Functional data analysis | - |
dc.subject | Exploratory data analysis | - |
dc.subject | Principal component analysis | - |
dc.title | Singular value decomposition and its visualization | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1198/106186007X256080 | - |
dc.identifier.scopus | eid_2-s2.0-38049153402 | - |
dc.identifier.volume | 16 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 833 | - |
dc.identifier.epage | 854 | - |
dc.identifier.isi | WOS:000252010500005 | - |
dc.identifier.issnl | 1061-8600 | - |