Simple Problem Formulation

In practice ICA boils down to the following problem:

Find the matrix $A$ which minimises the function $f(S)$, where $Y = A S$.

The function $f(\cdot)$ is chosen to be an empirical estimate of the statistical dependence between the rows of $S$ (the spatial maps). For instance, the functions which have been used to perform ICA include: (1) Mutual Information; (2) Negentropy and (3) a summary of a finite number of higher order moments/cumulants.