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The geometry of partial least squares

โœ Scribed by Aloke Phatak; Sijmen De Jong

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
437 KB
Volume
11
Category
Article
ISSN
0886-9383

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โœฆ Synopsis

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.

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