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

Mohamed Hanafi (1) , Samia Samar Ouertani (1, 2) , Julien Boccard (3, 4) , Gérard Mazerolles (5) , Serge Rudaz (3, 4)

1 StatSC - Statistique, Sensométrie et Chimiométrie
2 INRA - Institut National de la Recherche Agronomique
3 Ecole de Pharmacie
4 UNIL - Université de Lausanne = University of Lausanne
5 SPO - Sciences Pour l'Oenologie

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.

Mots clés: Multi-way data; Tensors; Multi-way PLS regression; Best rank-one approximation; Monotony sequences; data analysis

Mots clés: analyse de données

Domaines: Sciences du Vivant [q-bio]

Mohamed Hanafi, Samia Samar Ouertani, Julien Boccard, Gérard Mazerolles, Serge Rudaz. Multi-way PLS regression: monotony convergence of tri-linear PLS2 and optimality of parameters. Computational Statistics and Data Analysis, 2015, 83, pp.129-139. ⟨10.1016/j.csda.2014.10.003⟩. ⟨hal-01837731⟩