Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Partial Least-Squares Regression (PLSR)

Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_1274

Synonyms

Definition

Any exercise of mathematical regression aims to describe the behavior of a group of dependent variables (Y, responses block) as a function of a group of independent variables (X, predictors block). However, when there are more variables than observations or the predictors are correlated, ordinary multiple linear regressions (MLR) are not feasible. Partial-Least-Squares Regression (PLSR) provides a much more predictive linear-relationship, even in the case of a rank-deficient X matrix, and allows the simultaneous decomposition of X and Y blocks, thus facilitating a better understanding of the underlying structure (Geladi and Kowalski, 1986; Trygg, 2002; Höskuldsson 2004; Jørgensen and Goegebeur 2007; Varmuza and Filzmoser 2009).

PLSR Model

Any PLSR model is described by the following equations:
$$ {X_{{\rm n,p}}} = {\hat{X}_{{\rm n,p}}}+ {E_{{\rm n,p}}} = {T_{{\rm n,k}}}P_{{\rm k,p}}^{\rm T} + {E_{{\rm n,p}}} $$
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References

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  5. Jørgensen B, Goegebeur Y (2007) partial least squares regression (model PLS2). In: Multivariate data analysis and chemometrics. Departament Statistics. Syddansk University. Denmark. http://statmaster.sdu.dk/courses/STO2/module08/module.pdf. Accessed 2 Sept 2011
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Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.Department of Systems Biology and BioinformaticsInstitute of Computer Sciences, University of RostockRostockGermany
  2. 2.Department of Biochemistry and Molecular BiologyUniversity of La LagunaSan Cristóbal de La Laguna, Islas CanariasSpain