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PLS Leads to Different Algorithms for Factor Analysis and Regression

Holcomb, Tyler and Morari, Manfred (1993) PLS Leads to Different Algorithms for Factor Analysis and Regression. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1993.003

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Abstract

Two multivariable problems of general interest, are factor analysis and regression. This paper examines partial least squares (PLS) as a tool for both problems. For single output data sets, the familiar PLS algorithm is applicable to both problems. For multiple output problems the familiar PLS algorithm [1, 2, 3] (called fact-PLS in this paper) is appropriate for factor analysis. However fact-PLS leads to algebraically-inconistent results for regression problems. To address this issue, a new algebraically-consistent multivariable PLS algorithm, C-PLS, is developed. Unlike fact-PLS, C-PLS does not rely on iterative calculations. Another PLS approach, "one-at-a-time" PLS (OAT-PLS), is closely related to C-PLS; however OAT-PLS is also algebraically-inconsistent. A simulation study of these various PLS methods shows C-PLS to have the best estimation and prediction performance.


Item Type:Report or Paper (Technical Report)
Additional Information:Partiul support of this research through the Department of Energy, Office of Basic Energy Scicnces is gratefuly acknowledged.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1993.003
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1993.003
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28045
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:23 Jul 2006
Last Modified:26 Dec 2012 14:29

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