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

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  • Michel Tenenhaus

    (HEC Paris)

  • Arthur Tenenhaus

    (CentraleSupelec-L2S-Université Paris-Sud
    Brain and Spine Institute)

  • Patrick J. F. Groenen

    (Erasmus University)

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, $${\vert }x{\vert }$$ | x | , $$x^{2}$$ x 2 or $$x^{4}$$ x 4 and shrinkage constants 0 or 1, many multiblock component methods are recovered.

Suggested Citation

  • Michel Tenenhaus & Arthur Tenenhaus & Patrick J. F. Groenen, 2017. "Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 737-777, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-017-9573-x
    DOI: 10.1007/s11336-017-9573-x
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