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, (Formula presented.), (Formula presented.) or (Formula presented.) and shrinkage constants 0 or 1, many multiblock component methods are recovered.

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Keywords consensus PCA, GCCA, hierarchical PCA, MAXBET, MAXDIFF, MAXVAR, multiblock component methods, PLS path modeling, RGCCA, SSQCOR, SUMCOR
Persistent URL dx.doi.org/10.1007/s11336-017-9573-x, hdl.handle.net/1765/100190
Series ERIM Top-Core Articles
Journal Psychometrika
Tenenhaus, M. (Michel), Tenenhaus, A. (Arthur), & Groenen, P.J.F. (2017). Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods. Psychometrika, 1–41. doi:10.1007/s11336-017-9573-x