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Efficient cross-validatory computations and influence measures for principal component and partial least squares decompositions with applications in chemometrics

Mertens, Bart Josepha August; (1995) Efficient cross-validatory computations and influence measures for principal component and partial least squares decompositions with applications in chemometrics. Doctoral thesis (Ph.D), UCL (University College London). Green open access

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Abstract

The application of the efficient rank-one perturbation algebra of Bunch, Nielsen and Sorensen [BNS78] to the leave-one-out cross-validation of principal component regression is described. Similarly, we consider the restriction of the efficient leave-one-out cross-validatory algebra for continuum regression proposed by Stone and Brooks [SB90][SB92] to partial least squares regression. Implementations of both cross-validatory procedures are presented in the numerical analysis package GAUSS [Apt92], together with procedures for the computation of principal component and partial least squares regression equations. We describe the application to the leave-one-out cross-validatory assessment of principal component and partial least squares prediction equations, using near infrared spectroscopic data. The methodologies are compared with the existing procedures for efficiency and numerical accuracy. We derive influence measures from the cross-validatory computations and consider an application in food analysis on the use of near infrared spectroscopy for the calibration of total oil content of white mustard seeds. Finally, a published paper on the SIMCA [Wol76] method of classification which is based on the principal component decomposition and usually involves a cross-validatory assessment is bound in with this thesis, following the bibliography.

Type: Thesis (Doctoral)
Qualification: Ph.D
Title: Efficient cross-validatory computations and influence measures for principal component and partial least squares decompositions with applications in chemometrics
Open access status: An open access version is available from UCL Discovery
Language: English
Additional information: Thesis digitised by ProQuest.
URI: https://discovery.ucl.ac.uk/id/eprint/10105094
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