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Please use this identifier to cite or link to this item:
http://hdl.handle.net/2282/758
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| Title: | PLS post-processing by similarity transformation: a simple alternative to OPLS |
| Authors: | Ergon, Rolf |
| Issue Date: | 2005 |
| Publishers version: | http://dx.doi.org/10.1002/cem.899 |
| Abstract: | Several methods for orthogonal signal correction (OSC) based on pre-processing of the
modeling data have been developed in recent years, and OPLS (orthogonal projections to
latent structures) is a well known algorithm. The main result from these methods is a reduction
in the number of …nal components in partial least squares (PLS) regression, while the
predictions are virtually unchanged (identical for OPLS). This raises the question whether the
same or similar results can be obtained in a more direct way using an ordinary PLS model as
starting point, and as shown in the present paper this can indeed be done by use of a simple
similarity transformation. This post-processing PLS+ST method is compared with OPLS,
assuming a single response variable. The PLS+ST factorization of the data matrix X is just
a similarity transformation of the non-orthogonalized PLS factorization, while OPLS is a similarity
transformation of the orthogonalized PLS factorization. The predictions are therefore
identical, but the residuals are somewhat di¤erent. A theoretically founded modi…cation of
the orthogonalized PLS factorization, and a corresponding modi…cation of OPLS, leads to
identical factorizations for all these methods, within similarity transformations. The PLS+ST
vs. OPLS comparison also leads to an alternative post-processing method, using the ordinary
PLS algorithm twice, with predetermined and permuted loading weights vectors in the second
step. A limited comparison with post-processing using principal components of predictions
(PCP) or canonical correlation analysis (CCA) is included. |
| Keywords: | Orthogonal signal correction
OPLS
Post-processing
Similarity transformation |
| Publisher: | Wiley |
| Document type: | Journal article |
| URI: | http://hdl.handle.net/2282/758 |
| Appears in Collections: | Institutt for elektro, IT og kybernetikk
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