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PCR eigenvector selection based on correlation relative standard deviations
Author(s) -
Fairchild Steven Z.,
Kalivas John H.
Publication year - 2001
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.649
Subject(s) - eigenvalues and eigenvectors , mathematics , principal component analysis , selection (genetic algorithm) , standard deviation , correlation , statistics , algorithm , computer science , artificial intelligence , geometry , physics , quantum mechanics
While principal component regression (PCR) is often performed with eigenvectors ordered by decreasing singular values, PCR models have been formed using other eigenvector arrangements. A common criterion for organizing eigenvectors involves absolute correlations between respective eigenvectors and the prediction property being modeled. However, correlation cut‐off values for eigenvector selection are inconsistent between data sets, and additional criteria are needed such as the root mean square error of cross‐validation (RMSECV). Furthermore, correlations for some selected eigenvectors are often extremely low (e.g. values of 0·1 have been considered acceptable) and it is difficult to justify inclusion of these eigenvectors. Relative standard deviations (RSDs) of correlations are evaluated in this paper as an alternative method of eigenvector selection. This paper reveals distinct advantages for using eigenvectors ordered by RSDs of correlations compared to eigenvectors ordered by absolute correlations. In particular, RSDs can be used to determine significant eigenvectors without resorting to additional criteria such as the RMSECV. Additionally, inspection of RSD values explains why different correlation cut‐off values are obtained for different data sets as well as why correlations can be small. Copyright © 2001 John Wiley & Sons, Ltd.