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Multivariate calibration leverages and spectral F ‐ratios via the filter factor representation
Author(s) -
Andries Erik,
Kalivas John H.
Publication year - 2010
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.1277
Subject(s) - partial least squares regression , tikhonov regularization , principal component regression , calibration , multivariate statistics , filter (signal processing) , principal component analysis , chemometrics , regression , representation (politics) , mathematics , ridge , least squares function approximation , computer science , regularization (linguistics) , algorithm , statistics , artificial intelligence , mathematical analysis , inverse problem , geology , machine learning , estimator , politics , political science , law , computer vision , paleontology
Diagnostics are fundamental to multivariate calibration (MC). Two common diagnostics are leverages and spectral F ‐ratios and these have been formulated for many MC methods such as partial least square (PLS), principal component regression (PCR) and classical least squares (CLS). While these are some of the most common methods of calibration in analytical chemistry, ridge regression is also common place and yet spectral F ‐ratios have not been developed for it. Noting that ridge regression is a form of Tikhonov regularization (TR) and using the unifying filter factor representation for MC, this paper develops the filter factor form of leverages and spectral F ‐ratios. The approach is applied to a spectral data set to demonstrate computational speed‐up advantages and ease of implementation for the filter factor representation. Copyright © 2010 John Wiley & Sons, Ltd.