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Trendafilov, Nickolay
(2010).
DOI: https://doi.org/10.1016/j.csda.2010.03.010
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.
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About
- Item ORO ID
- 49279
- Item Type
- Journal Item
- ISSN
- 1872-7352
- Keywords
- simultaneous diagonalization; dimensionality reduction; power iterations for k symmetric positive definite matrices
- Academic Unit or School
-
Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2010 Elsevier B.V.
- Depositing User
- Nickolay Trendafilov