ICA on the PCA Reduced Data

As any collection of independent spatial maps will also be uncorrelated, the ICA result will lie in the decorrelation manifold. That is, the ICA problem can be written as one of finding the matrix $Q$ from the previous section such that $f(S_2)$ is minimised.

So the problem is to find the orthogonal matrix $Q$ such that $f(S_2)$ is minimised where $Y_R = Q S_2$.

Note that the term `unmixing matrix' is often used in ICA and refers to $W = Q^{-1}$ for the reduced data or $W = (A_1 Q)^{-1}$ for the full data.