concorGMCANO - Canonical analysis of subsets Yj with subsets Xi.
X and Y are 2 data matrices, n x p and n x q, of p variables and q variables (centered).
The row vector px contains the kx numbers of variables of the kx subsets of X.
The row vector py contains the ky numbers of variables of the ky subsets of Y. sum(px)=p and sum(py)=q.
When kx =1 (px=p), use concorCANO.m
r is the wanted number of solutions (< 1+min(rank(Xi'Yj))).
The kx blocks ui (rx(i) x r) of u, are formed with r orthonormed vectors.
P1=P(:,1:rx(1)), P2=P(:,rx(1)+1 : rx(1)+rx(2)), P3 =....
Each matrix Xi has been standardized for obtaining the matrix Pi and the standardized canonical components Piui.
P1=P(:,1:rx(1)), P2=P(:,rx(1)+1 : rx(1)+rx(2)), P3 =....
P1u1=P(:,1:rx(1))*u(1:rx(1),:).
Idem for Py, ry , and v.
For each pair (Xi,Yj), and each solution k, rho2 contains the squared correlations rho2ijk=rho2(Piui(:,k),Yjvj(:,k)).
For each solution k, sumi sumj rho2ijk is the optimized criterion,
px+py orthogonality constraints for a new solution : ui'*ui=Ir and vj'*vj=Ir.
Kissita G. Thesis Paris 9 (2003) gakissita@yahoo.fr