PLS and dimension reduction for classification |
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Authors: | Yushu Liu William Rayens |
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Institution: | (1) Department of Statistics, University of Kentucky, 865 Patterson Office Tower, Lexington, KY 40506, USA |
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Abstract: | Barker and Rayens (J Chemometrics 17:166–173, 2003) offered convincing arguments that partial least squares (PLS) is to be
preferred over principal components analysis (PCA) when discrimination is the goal and dimension reduction is required, since
at least with PLS as the dimension reduction tool, information involving group separation is directly involved in the structure
extraction. In this paper the basic results in Barker and Rayens (J Chemometrics 17:166–173, 2003) are reviewed and some of
their ideas and comparisons are illustrated on a real data set, something which Barker and Rayens did not do. More importantly,
new results are introduced, including a formal proof for the superiority of PLS over PCA in the two-group case, as well as
new connections between PLS for discrimination and an extended class of PLS-like techniques known as “oriented PLS” (OrPLS).
In the latter case, a particularly simple subclass of OrPLS procedures, when used to achieve the dimension reduction, is shown
to always produce a lower misclassification rate than when “ordinary” PLS is used for the same purpose. |
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Keywords: | Linear discriminant analysis Ridge regression Shrinkage estimation Misclassification rates Principal components |
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