- Partial least squares regression
In

statistics , the method of**partial least squares regression (PLS-regression)**bears some relation toprincipal component analysis ; instead of finding thehyperplane s of minimumvariance , it finds alinear model describing somepredicted variable s in terms of otherobservable variable s.It is used to find the fundamental relations between two matrices ("X" and "Y"), i.e. a

latent variable approach to modeling thecovariance structures in these two spaces. A PLS model will try to find the multidimensional direction in the "X" space that explains the maximum multidimensional variance direction in the "Y" space. Partial least squares is particularly suited when the matrix of predictors has more variables than observations (seemulticollinearity ). By contrast, standard regression will fail in these cases.It was first introduced by the Swedish statistician

Herman Wold . An alternative (and arguably, more correct, according to Wold) long form for PLS is**projection to latent structures**but the term**partial least squares**is still dominant in some areas. It is widely applied in the field ofchemometrics , in sensory evaluation, and more recently, inchemical engineering process data (seeJohn F. MacGregor ) and the analysis of functional brain imaging data(see [Randy McIntosh] ).**ee also***

Feature extraction

*Data mining

*Machine learning

*Regression analysis **References***cite paper | author=Frank, Ildiko and Jerome Friedman (1993) | title=A Statistical View of Some Chemometrics Regression Tools, Technometrics, 35(2), pp 109–148 | year=1993

*cite paper | author=Haenlein, Michael and Andreas M. Kaplan (2004) | title=A Beginner's Guide to Partial Least Squares Analysis, Understanding Statistics, 3(4), 283–297| year=2004

*cite paper | author=Henseler, Joerg and Georg Fassott (2005) | title=Testing Moderating Effects in PLS Path Models. An Illustration of Available Procedures| year=2005

*cite paper | author=Lingjærde, Ole-Christian and Nils Christophersen (2000) | title=Shrinkage Structure of Partial Least Squares, Scandinavian Journal of Statistics, 27(3), pp 459–473 | year=2000

*cite book | author=Tenenhaus Michel | title= La Regression PLS: Theorie et Pratique. Paris: Technip.| year=1998**External links*** [

*http://support.sas.com/rnd/app/da/new/dapls.html PLS at SAS*]

* [*http://cisrg.shef.ac.uk/people/jewelln/Regression%20Tutorial/index.htm PLS and regression tutorial*]

* [*http://www.rotman-baycrest.on.ca/pls PLS in Brain Imaging*]

* [*http://www.vcclab.org/lab/pls on-line PLS*] regression (PLSR) at Virtual Computational Chemistry Laboratory

* [*http://www.chemometry.com/Research/MVC.html Uncertainty estimation for PLS*]

* [*http://www.utd.edu/~herve/Abdi-PLSR2007-pretty.pdf A short introduction to PLS regression and its history*]

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