Tenenhaus Michel, Tenenhaus Arthur, Groenen Patrick J F
HEC Paris, Jouy-en-Josas, France.
Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), CentraleSupelec-L2S-Université Paris-Sud, 3 rue Joliot-Curie, Plateau du Moulon, 91192 , Gif-sur-Yvette Cedex, France.
Psychometrika. 2017 May 23. doi: 10.1007/s11336-017-9573-x.
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: see text], [Formula: see text] or [Formula: see text] and shrinkage constants 0 or 1, many multiblock component methods are recovered.
提出了一种用于序列多块分量方法的新框架。该框架依赖于正则化广义典型相关分析（RGCCA）的新版本，其中考虑了各种方案函数和收缩常数。考虑了两种类型的块间连接：块要么完全连接，要么连接到超块（所有块的串联）。所提出的迭代算法是单调收敛的，并保证在收敛时获得RGCCA的一个驻点。在某些情况下，RGCCA的解是某个矩阵的第一个特征值/特征向量。对于方案函数x、[公式：见正文]、[公式：见正文]或[公式：见正文]以及收缩常数0或1，可以恢复许多多块分量方法。
