svdbips {BMconcor} | R Documentation |
SVD for bipartitioned matrix x
Description
SVD for bipartitioned matrix x. SIMULTANEOUS SOLUTIONS. ("simultaneous svdbip")
Usage
svdbips(x, K, H, r)
Arguments
x |
a |
K |
is a row vector which contains the numbers pk, k=1,...,kx, of the partition of x with kx row blocks : |
H |
is a row vector which contains the numbers qh, h=1,...,ky, of the partition of x with ky column blocks : sum(qh)=q |
r |
The number of wanted successive solutions |
Details
One set of r solutions is calculated by maximizing \sum_i \sum_k \sum_h
(u_k[,i]'*x_{kh}*v_h[,i])^2
, with kx+ky orthonormality constraints (for
each uk and each vh). For each fixed r value, the solution is totally
new (does'nt consist to complete a previous calculus of one set of r-1
solutions). rmax=min([min(K),min(H)])
. When r=1, it is svdbip (thus
it is svdcp when r=1 and kx=1).
Convergence of algorithm may be not global. So the below proposed
initialisation of the algorithm may be not very suitable for some data
sets. Several different random initialisations with normed vectors
might be considered and the best result then choosen....
Value
A list
with following components:
u |
a |
v |
a |
s |
a |
Author(s)
Lafosse, R.
References
Lafosse R. & Ten Berge J. A simultaneous CONCOR method for the analysis of two partitioned matrices. submitted.
Examples
x <- matrix(runif(200),10,20)
s1 <- svdbip(x,c(3,4,3),c(5,5,10),2);sum(sum(sum(s1$s2)))
ss <- svdbips(x,c(3,4,3),c(5,5,10),2);sum(sum(sum(ss$s2)))