concorgmcano function

Canonical analysis of subsets Yj with subsets Xi

Canonical analysis of subsets Yj with subsets Xi. Relative valuations by squared correlations of the proximities of subsets Xi with subsets Yj. SUCCESSIVE SOLUTIONS

concorgmcano(x, px, y, py, r)

Arguments

• x: are the n times p and n times q matrices of p and q centered column
• px: The row vector which contains the numbers pi, i=1,...,kx, of the kx subsets xi of x : $\sum_i p_i$=sum(px)=p. px is the partition vector of x
• y: See x
• py: The partition vector of y. A row vector containing the numbers qi for i = 1,...,ky of the ky subsets yi of y : sum(qi)=sum(py)=q.
• r: The number of wanted successive solutions rmax <= min(min(px),min(py),n)

Returns

A list with following components: - cx: is a n.kx times r matrix of kx row blocks cxi (n x r). Each row block contains r partial canonical components

• cy: is a n.ky times r matrix of ky row blocks cyj (n x r). Each row block contains r partial canonical components

• rho2: is a kx time ky tims r array; for a fixed solution k, rho2[,,k] contains kxky squared correlations $rho2(cx[n*(i-1)+1:n*i,k],cy[n*(j-1)+1:n*j,k])$, simultaneously calculated between all the yj with all the xi

Details

For the first solution, $sum_i sum_j \mbox{rho2}(cx_i[,1],cy_j[,1])$ is the optimized criterion. The other solutions are calculated from the same criterion, but with orthogonalities for having two by two zero correlated the canonical components defined for each xi, and also for those defined for each yj. Each solution associates kx canonical components to ky canonical components. When kx =1 (px=p), take concorcano function This function uses the concorgm function

Examples

x <- matrix(runif(50),10,5);y <- matrix(runif(90),10,9)
x <- scale(x);y <- scale(y)
cc <- concorgmcano(x,c(2,3),y,c(3,2,4),2)
cc$rho2[1,1,]

References

Kissita G., Analyse canonique generalisee avec tableau de reference generalisee. Thesis, Ceremade Paris 9 Dauphine (2003).

Author(s)