Multi-way PLS for discrimination: Compact form equivalent to the tri-linear PLS2 procedure and its monotony convergence

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

1 StatSC - Statistique, Sensométrie et Chimiométrie
2 SPO - Sciences Pour l'Oenologie
3 School of Pharmaceutical Sciences

This paper focuses on multi-way PLS for discrimination. Emphasis was placed on the computation of parameters (so-called scores and loadings) using an iterative procedure called tri-linear PLS2. In the context of discrimination, this algorithm is applied to a dummy matrix representing group membership, and according to its specific formalism, the tri-linear PLS2 procedure offers the possibility of simplification. The purpose of this paper is to introduce a compact formulation of the tri-linear PLS2 procedure adapted for a discrimination setting. A property of this variant that allows formally establishing its convergence and, by extension, the convergence of the tri-linear PLS2 will be demonstrated. The potential of this compact form will be illustrated with simulated examples.

Mots clés: Multi-way PLS regression; Discriminant analysis; Tri-linear PLS2; Three-way data; PARTIAL LEAST-SQUARES; MULTILINEAR PLS; REGRESSION; CHEMOMETRICS; COMPONENTS; DA

Domaines: Sciences du Vivant [q-bio]

Samia Samar Ouertani, Gerard Mazerolles, Julien Boccard, Serge Rudaz, Mohamed Hanafi. Multi-way PLS for discrimination: Compact form equivalent to the tri-linear PLS2 procedure and its monotony convergence. Chemometrics and Intelligent Laboratory Systems, 2014, 133, pp.25 - 32. ⟨10.1016/j.chemolab.2014.01.015⟩. ⟨hal-01837700⟩