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Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods

Published online by Cambridge University Press:  01 January 2025

Michel Tenenhaus ,
Arthur Tenenhaus Open the ORCID record for Arthur Tenenhaus [Opens in a new window]  and
Patrick J. F. Groenen
Michel Tenenhaus
Affiliation:
HEC Paris
Arthur Tenenhaus*
Affiliation:
CentraleSupelec-L2S-Université Paris-Sud Brain and Spine Institute
Patrick J. F. Groenen
Affiliation:
Erasmus University
*
Correspondence should be made to Arthur Tenenhaus, Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), CentraleSupelec-L2S-Université Paris-Sud, 3 rue Joliot-Curie, Plateau du Moulon, 91192 Gif-sur-Yvette Cedex, France. Email: [email protected]
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Abstract

A new framework for sequential multiblock component methods is presented. This framework relies on a new version of regularized generalized canonical correlation analysis (RGCCA) where various scheme functions and shrinkage constants are considered. Two types of between block connections are considered: blocks are either fully connected or connected to the superblock (concatenation of all blocks). The proposed iterative algorithm is monotone convergent and guarantees obtaining at convergence a stationary point of RGCCA. In some cases, the solution of RGCCA is the first eigenvalue/eigenvector of a certain matrix. For the scheme functions x, |x|\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\vert }x{\vert }$$\end{document}, x2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x^{2}$$\end{document} or x4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$x^{4}$$\end{document} and shrinkage constants 0 or 1, many multiblock component methods are recovered.

Keywords

consensus PCAhierarchical PCAMAXBETMAXDIFFMAXVARmultiblock component methodsPLS path modelingGCCARGCCASSQCORSUMCOR
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 737 - 777
Copyright
Copyright © 2017 The Psychometric Society

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