期刊
COMPUTATIONAL STATISTICS & DATA ANALYSIS
卷 56, 期 6, 页码 1869-1879出版社
ELSEVIER
DOI: 10.1016/j.csda.2011.11.012
关键词
PCA; Number of components; Cross-validation; Smoothing matrix; Generalized cross-validation
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. Crown Copyright (c) 2011 Published by Elsevier B.V. All rights reserved.
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