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

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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