Trendafilov, Nickolay T.
(2010).
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| DOI (Digital Object Identifier) Link: | http://dx.doi.org/doi:10.1016/j.csda.2010.03.010 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
The standard common principal components (CPCs) may not always be useful for simultaneous dimensionality reduction in k groups. Moreover, the original FG algorithm finds the CPCs in arbitrary order, which does not reflect their importance with respect to the explained variance. A possible alternative is to find an approximate common subspace for all k groups. A new stepwise estimation procedure for obtaining CPCs is proposed, which imitates standard PCA. The stepwise CPCs facilitate simultaneous dimensionality reduction, as their variances are decreasing at least approximately in all k groups. Thus, they can be a better alternative for dimensionality reduction than the standard CPCs. The stepwise CPCs are found sequentially by a very simple algorithm, based on the well-known power method for a single covariance/correlation matrix. Numerical illustrations on well-known data are considered.
| Item Type: | Journal Article |
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| Copyright Holders: | 2010 Elsevier B.V. |
| ISSN: | 0167-9473 |
| Keywords: | simultaneous diagonalization; dimensionality reduction; power iterations for k symmetric positive definite matrices |
| Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: | 20904 |
| Depositing User: | Sarah Frain |
| Date Deposited: | 20 Jul 2010 11:52 |
| Last Modified: | 17 May 2013 03:46 |
| URI: | http://oro.open.ac.uk/id/eprint/20904 |
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