Regularized Consensus PCA

M Tenenhaus, A Tenenhaus, Patrick Groenen

Research output: Book/Report/Inaugural speech/Farewell speechReportAcademic

Abstract

A new framework for many multiblock component methods (including consensus and hierarchical PCA) is proposed. It is based on the consensus PCA model: a scheme connecting each block of variables to a superblock obtained by concatenation of all blocks. Regularized consensus PCA is obtained by applying regularized generalized canonical correlation analysis to this scheme for the function g(x) = x^m where m >= 1. A gradient algorithm is proposed. At convergence, a solution of the stationary equation related to the optimization problem is obtained. For m = 1, 2 or 4 and shrinkage constants equal to 0 or 1, many multiblock component methods are recovered.
Original languageEnglish
Publication statusPublished - 2015

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