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Generalized orthogonal multiple co‐inertia analysis(–PLS): new multiblock component and regression methods
Author(s) -
Vivien Myrtille,
Sabatier Robert
Publication year - 2003
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.802
Subject(s) - component analysis , normalization (sociology) , partial least squares regression , principal component analysis , component (thermodynamics) , mathematics , regression , computer science , inertia , algorithm , mathematical optimization , artificial intelligence , statistics , physics , classical mechanics , sociology , anthropology , thermodynamics
The purpose of this paper is to develop new component‐wise component and regression multiblock methods that overcome some of the difficulties traditionally associated with multiblocks, such as the step‐by‐step optimization and component orthogonalities. Generalized orthogonal multiple co‐inertia analysis (GOMCIA) and generalized orthogonal multiple co‐inertia analysis–partial least squares (GOMCIA–PLS) are proposed for modelling two sets of blocks measured on the same observations. We especially emphasize GOMCIA–PLS methods in which we consider one of the sets as predictive. All these methods are based on the step‐by‐step maximization of the same criterion under normalization constraints and produce orthogonal components or super‐components. The solutions of the problem have to be computed with an iterative algorithm (which we prove to be convergent). We also give some interesting special cases and discuss the differences compared with a few other multiblock and/or multiway methods. Finally, short examples of real data are processed to show how GOMCIA–PLS can be used and its properties. Copyright © 2003 John Wiley & Sons, Ltd.