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

Michel Tenenhaus (), Arthur Tenenhaus () and Patrick Groenen ()
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Michel Tenenhaus: HEC Paris
Arthur Tenenhaus: CentraleSupelec-L2S-Université Paris-Sud

Psychometrika, 2017, vol. 82, issue 3, No 10, 737-777

Abstract: 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.

Keywords: consensus PCA; hierarchical PCA; MAXBET; MAXDIFF; MAXVAR; multiblock component methods; PLS path modeling; GCCA; RGCCA; SSQCOR; SUMCOR (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11336-017-9573-x

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