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Multi-way PLS regression: Monotony convergence of tri-linear PLS2 and optimality of parameters

Author

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  • Hanafi, Mohamed
  • Ouertani, Samia Samar
  • Boccard, Julien
  • Mazerolles, Gérard
  • Rudaz, Serge

Abstract

The tri-linear PLS2 iterative procedure, an algorithm pertaining to the NIPALS framework, is considered. It was previously proposed as a first stage to estimate parameters of the multi-way PLS regression method. It is shown that the tri-linear PLS2 procedure is convergent. The procedure generates a sequence of parameters (scores and loadings), which can be described as increasing or decreasing two specific criteria. Furthermore, a hidden tensor is described allowing tri-linear PLS2 to search its best rank-one approximation. This tensor highlights the link between multi-way PLS regression and the well-known PARAFAC model. The parameters of the multi-way PLS regression method can be computed using three alternative procedures.

Suggested Citation

  • Hanafi, Mohamed & Ouertani, Samia Samar & Boccard, Julien & Mazerolles, Gérard & Rudaz, Serge, 2015. "Multi-way PLS regression: Monotony convergence of tri-linear PLS2 and optimality of parameters," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 129-139.
    • Handle: RePEc:eee:csdana:v:83:y:2015:i:c:p:129-139
    DOI: 10.1016/j.csda.2014.10.003
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    1. T. Andrew Clayton & John C. Lindon & Olivier Cloarec & Henrik Antti & Claude Charuel & Gilles Hanton & Jean-Pierre Provost & Jean-Loïc Le Net & David Baker & Rosalind J. Walley & Jeremy R. Everett & J, 2006. "Pharmaco-metabonomic phenotyping and personalized drug treatment," Nature, Nature, vol. 440(7087), pages 1073-1077, April.
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