Selecting the number of components in principal component analysis using cross-validation approximations
AbstractCross-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 InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Computational Statistics & Data Analysis.
Volume (Year): 56 (2012)
Issue (Month): 6 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/csda
PCA; Number of components; Cross-validation; Smoothing matrix; Generalized cross-validation;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dray, Stephane, 2008. "On the number of principal components: A test of dimensionality based on measurements of similarity between matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2228-2237, January.
- Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer, vol. 62(2), pages 251-266, June.
- Ferre, Louis, 1995. "Selection of components in principal component analysis: A comparison of methods," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 669-682, June.
- Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
- Julie Josse & Jérôme Pagès & François Husson, 2011. "Multiple imputation in principal component analysis," Advances in Data Analysis and Classification, Springer, vol. 5(3), pages 231-246, October.
- Peres-Neto, Pedro R. & Jackson, Donald A. & Somers, Keith M., 2005. "How many principal components? stopping rules for determining the number of non-trivial axes revisited," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 974-997, June.
- Chunlei Ke & Yuedong Wang, 2004. "Smoothing Spline Nonlinear Nonparametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1166-1175, December.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.