Regularized Consensus PCA

M Tenenhaus; A Tenenhaus; Patrick Groenen

Regularized Consensus PCA

M Tenenhaus, A Tenenhaus, Patrick Groenen

Econometrics

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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 >= 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 language	English
Publisher	arXiv
Publication status	Published - 2015

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EUR ESE 31

Cite this

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title = "Regularized Consensus PCA",

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.",

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year = "2015",

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TY - BOOK

T1 - Regularized Consensus PCA

AU - Tenenhaus, M

AU - Tenenhaus, A

AU - Groenen, Patrick

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

UR - http://arxiv.org/abs/1504.07005

M3 - Report

BT - Regularized Consensus PCA

PB - arXiv

ER -

Regularized Consensus PCA

Abstract

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