[R] Maximally independent variables

[Gabor Grothendieck]

Are there any R packages that relate to the
following data reduction problem fo finding
maximally independent variables?

Currently what I am doing is solving the following
minimax problem:  Suppose we want to find the
three maximally independent variables.  From the
full n by n correlation matrix, C, of all n variables
chooose three variables and form their 3 by 3 correlation
submatrix, C1, finding the offdiagonal entry of C1
which is largest in absolute value.  Call that z.  Thus for
each set of 3 variables we can associate such a z.
Now for each possible set of three variables find the one for
which its value of z is least.

I only give the above formulation because that is
what I am doing now but I would be happy to
consider other different formulations.