Abstract
A simple way to develop non-linear PLS models is presented, INLR (implicit non-linear latent variable regression). The paper shows that by simply added squared x-variables x2a, both the square and cross terms of the latent variables are implicitly included in the resulting PLS model. This approach works when X itself is well modelled by a projection model T*PT. Hence, if a latent structure is present in X, it is not necessary to include the cross terms of the X-variables in the polynomial expansion. Analogously, with cubic non-linearities, expanding X with cubic terms x3a is sufficient. INLR is attractive in that all essential features of PLS are preserved i.e. (a) it can handle many noisy and collinear variables, (b) it is stable and gives reliable results and (c) all PLS plots and diagnostics still apply. The principles of INLR are outlined and illustrated with three chemical examples where INLR improved the modelling and predictions compared with ordinary linear PLS. © 1997 John Wiley & Sons, Ltd.
Keywords
Latent variableLinear regressionProjection (relational algebra)MathematicsPolynomialVariable (mathematics)Latent variable modelOrdinary least squaresVariablesApplied mathematicsRegression analysisRegressionSimple (philosophy)StatisticsAlgorithmMathematical analysis
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Publication Info
- Year
- 1997
- Type
- article
- Volume
- 11
- Issue
- 2
- Pages
- 141-156
- Citations
- 110
- Access
- Closed
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Cite This
Anders Berglund,
Svante Wold
(1997).
INLR, implicit non-linear latent variable regression.
Journal of Chemometrics
, 11
(2)
, 141-156.
https://doi.org/10.1002/(sici)1099-128x(199703)11:2<141::aid-cem461>3.0.co;2-2
Identifiers
- DOI
- 10.1002/(sici)1099-128x(199703)11:2<141::aid-cem461>3.0.co;2-2