Selecting the number of components in principal component analysis using cross-validation approximations
Abstract
Cross-validation is a tried and tested approach to select the number of components in principal component analysis (PCA), however, its main drawback is its computational cost. In a regression (or in a non parametric regression) setting, criteria such as the general cross-validation one (GCV) provide convenient approximations to leave-one-out cross-validation. They are based on the relation between the prediction error and the residual sum of squares weighted by elements of a projection matrix (or a smoothing matrix). Such a relation is then established in PCA using an original presentation of PCA with a unique projection matrix. It enables the definition of two cross-validation approximation criteria: the smoothing approximation of the cross-validation criterion (SACV) and the GCV criterion. The method is assessed with simulations and gives promising results.Download Info
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Bibliographic Info
Article provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 6 ()
Pages: 1869-1879
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Web page: http://www.elsevier.com/locate/csda
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Keywords: PCA; Number of components; Cross-validation; Smoothing matrix; Generalized cross-validation;References
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