The geometry of partial least squares

Autor:	Aloke Phatak, Sijmen de Jong
Rok vydání:	1997
Předmět:	Applied Mathematics Non-linear least squares Partial least squares regression Oblique projection Ordinary least squares Symmetric matrix Geometry Rotation (mathematics) Ellipsoid Eigenvalues and eigenvectors Analytical Chemistry Mathematics
Zdroj:	Journal of Chemometrics. 11:311-338
ISSN:	1099-128X 0886-9383
DOI:	10.1002/(sici)1099-128x(199707)11:4<311::aid-cem478>3.0.co;2-4
Popis:	Our objective in this article is to clarify partial least squares (PLS) regression by illustrating the geometry of NIPALS and SIMPLS, two algorithms for carrying out PLS, in both object and variable space. We introduce the notion of the tangent rotation of a vector on an ellipsoid and show how it is intimately related to the power method of finding the eigenvalues and eigenvectors of a symmetric matrix. We also show that the PLS estimate of the vector of coefficients in the linear model turns out to be an oblique projection of the ordinary least squares estimate. With two simple building blocks—tangent rotations and orthogonal and oblique projections—it becomes possible to visualize precisely how PLS functions. © 1997 John Wiley & Sons, Ltd.
Databáze:	OpenAIRE
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