f.icast.fmri(foncfile,maskfile,is.spatial,n.comp.compute=TRUE,n.comp=0,hp.filter=TRUE)The data matrix is considered to be a linear combination of non-Gaussian (independent) components i.e. X = AS where rows of S contain the independent components and A is a linear mixing matrix. In short ICA attempts to 'un-mix' the data by estimating an un-mixing matrix U where UX = S.
Under this generative model the measured 'signals' in X will tend to be 'more Gaussian' than the source components (in S) due to the Central Limit Theorem. Thus, in order to extract the independent components/sources we search for an un-mixing matrix U that maximizes the non-gaussianity of the sources.
In FastICA, non-gaussianity is measured using approximations to negentropy (J) which are more robust than kurtosis based measures and fast to compute.
The approximation takes the form
$J(y)=[E{G(y)}-E{G(v)}]^2$ where $v$ is a N(0,1) r.v
The following choices of G are included as options $G(u)=\frac{1}{\alpha} \log \cosh (\alpha u)$ and $G(u)=-\exp(\frac{-u^2}{2})$
The FastICA algorithm is used to 'un-mix' the data and recover estimates of the mixing matrix A and the source matrix S. Rows of the source matrix S represent spatially independent components of the dataset (these are arranged spatially in the output). Columns of A contain the associated time-courses of the independent components.
Pre-processing involves removing the mean of each row of the data matrix and (optionally) standardizing the columns of the data matrix to have zero mean and unit variance.
All computations are done using C code. This avoids reading the entire dataset into R and thus saves memory space.
f.icast.fmri.gui