From multiblock partial least squares to multiblock redundancy analysis. A continuum approach. (English) Zbl 1263.62093

Bougeard, Stéphanie; Qannari, El Mostafa; Lupo, Coralie; Hanafi, Mohamed

Informatica, Vilnius 22, No. 1, 11-26 (2011).

Summary: For the purpose of exploring and modelling the relationships between a data set and several data sets, multiblock partial least squares is a widely used regression technique. It is designed as an extension of PLS which aims at linking two data sets. In the same vein, we propose an extension of redundancy analysis to the multiblock setting. We show that PLS and multiblock redundancy analysis aim at maximizing the same criterion but the constraints are different. From the solutions of both these approaches, it turns out that they are the two end points of a continuum approach that we propose to investigate.

MSC:

62H12	Estimation in multivariate analysis
62J05	Linear regression; mixed models
65C60	Computational problems in statistics (MSC2010)

Keywords:

continuum approach; ridge-type regularization; multicollinearity