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

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

Computational Statistics & Data Analysis, 2015, vol. 83, issue C, 129-139

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.

Keywords: Multi-way data; Tensors; Multi-way PLS regression; Best rank-one approximation; Monotony sequences (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:83:y:2015:i:c:p:129-139

DOI: 10.1016/j.csda.2014.10.003

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