Scilab Function

concorCANO - Canonical analysis between one subset X and several subsets Yj

Calling Sequence

[P,u,Py,ry,v,V,rho2]=concorCANO(X,Y,py,r)

Description

X and Y are 2 data matrices, n x p and n x q, of p variables and q variables (centered). The row vector py contains the ky numbers of variables of the ky subsets of Y. sum(py)=q. Y is the concatenated matrix of matrices Yj, j=1,...,ky. r is the wanted number of solutions [0

P is a matrix with n rows which is obtained from X by standardization.

Py is a matrix with n rows which contains the standardized matrices Pyj respectively associated to Yj. The number of the columns of Pyj is ry(j).

The r columns of P*u are the r canonical variables relative to X. v contains ky blocks vj, each of them with r columns. v1=v(1:ry(1),:), v2=v(ry(1)+1:ry(1)+ry(2),:), ...

Pyj*vj are the r canonical variables of Yj, respectively associated with the r canonical variables of X.

For each set, the canonical variables are standardized and 2 by 2 zero correlated.

rho2 (ky x r) contains the canonical coefficients rho2(Yjvj(:,k),Pu(:,k)) associated to the solution k, k=1, ...r.

The total sum of squared correlations of the the first solution is maximal.

Py*V contains (for each k) weighted means of the Pyj*vj (the weights, are for each fixed k, rho(Yjvj(:,k),Pu(:,k)). For the set of r solutions, the matrix (P*u)'Py*V is diagonal. The matrices (Pu)'Pyjvj are triangular.

diag((P*u)'*Py*V/n)'.^2 = sum(rho2,1)

Authors

Hanafi & Lafosse (2001) in Revue de Statistique Appliquee vol.49, n.1. hanafi@enitiaa-nantes.fr Roger.Lafosse@lsp.ups-tlse.fr