Double restricted Co‐Inertia Analysis

Abstract

In this paper, an extension of the Co‐Inertia Analysis 1 is proposed. This extension is based on an objective function which takes directly into account the external information, as linear restrictions, about parameters of both sets of variables, by rewriting the Co‐Inertia Analysis objective function according to the principle of Restricted Eigenvalue Problem 2. A restricted extension of Wold's two‐block ‘Mode A’ Partial Least Squares 3 is also proposed. Copyright © 2007 John Wiley & Sons, Ltd.

Generalized constrained co-inertia analysis

“…We remark that, in this new proposal of constrained co-inertia analysis likewise in the others, all linear constraints are imposed by the reparametrization method. If we define the constraint matrices Z X and Z Y according to the null space method (that is B and Z), then this constrained COA amounts also to obtaining GSVD(P ⊥ B X T DYP ⊥ Z ) which is analogous to double restricted co-inertia analysis (hereafter DRCOA) by Amenta (2007) with Q X = I p and Q Y = I q . The underlying optimization problem for this last constrained analysis is max cov 2 (Xw i , Yc i ) where the unknown weight vectors w i and c i satisfy the constraints w…”