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Principal Component Analysis with External Information on both Subjects and Variables
Abstract
A method for structural analysis of multivariate data is proposed that combines features of regression analysis and principal component analysis. In this method, the original data are first decomposed into several components according to external information. The components are then subjected to principal component analysis to explore structures within the components. It is shown that this requires the generalized singular value decomposition of a matrix with certain metric matrices. The numerical method based on the QR decomposition is described, which simplifies the computation considerably. The proposed method includes a number of interesting special cases, whose relations to existing methods are discussed. Examples are given to demonstrate practical uses of the method.
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Cited by
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Dolédec, S., Chessel, D., ter Braak, C. J. F., & Champely, S. (1996) · Environmental and Ecological Statistics · doi:10.1007/bf02427859 · Cited by 731
(2004) · Springer Texts in Statistics · doi:10.1007/b98963 · Cited by 517
Ranger, M., Chau, C. M. Y., Garg, A., Woodward, T. S., Beg, M. F., Bjornson, B., Poskitt, K., Fitzpatrick, K., Synnes, A. R., Miller, S. P., et al. (2013) · PLoS ONE · doi:10.1371/journal.pone.0076702 · Cited by 288
Preference mapping in practice
Greenhoff, K., & MacFie, H. J. H. (1994) · Measurement of Food Preferences · doi:10.1007/978-1-4615-2171-6_6 · Cited by 265
Goghari, V. M., Sanford, N., Spilka, M. J., & Woodward, T. S. (2017) · Schizophrenia Bulletin · doi:10.1093/schbul/sbx004 · Cited by 38
Metadata
- Authors
- Takane, Y., & Shibayama, T.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1991-03
- Volume
- 56
- Issue
- 1
- Pages
- 97-120
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2154388264
- Cited by
- 186
- References
- 0
- FWCI
- 4.01
- Type
- journal article
- Language
- en
- Open access
- closed
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