If you think of the IC's as an input-output device (linear transformaton), where balance weights get transformed into vibration responses to be superimposed on the initial vibration then the SVD (singular value decomposition) of the IC matrix breaks down the IC matrix into input and output components. The components are ranked by the singular values as to the affect they have. The input components relate to the balance weights and the output components relate to the output directions or the vibration responses.

Let H=IC's then H can be written by a SVD as
H=U*S*V' where U is a matrix of output (vibration) response directions and V has the corresponding balance weight distributions. S is a diagnonal matrix of singular values, the relative importance of the balance weight distributions.

On the www, I find the following resources.
http://www.uwlax.edu/faculty/will/svd/index.html
http://mathworld.wolfram.com/SingularValueDecomposition.html

http://en.wikipedia.org/wiki/Singular_value_decomposition

Plus lots more.