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arXiv · 1504.07005

Regularized Consensus PCA

Michel Tenenhaus·Arthur Tenenhaus·Patrick J. F. Groenen
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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 $m \ge 1$. 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.

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Michel Tenenhaus, Arthur Tenenhaus, Patrick J. F. Groenen. 2015-04-27. Regularized Consensus PCA. https://arxiv.org/abs/1504.07005

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