Probabilistic Independent Component Analysis in FMRI
C. F. Beckmannit, S. M. Smitht · 2002
Independent Component Analysis (ICA) is classically performed using a square and noise-free mixing model, where the number of observations equals the number of source processes. In FMRI, both assumptions are known to be invalid and conflict with the model assumptions of the standard general linear model. We employ a probabilistic ICA (PICA) model for FMRI data that allows for more gen- eral non-square mixing in the presence of isotropic Gaussian noise and compare its performance against the conventional noise-free model. In the probabilistic ICA model, the normalized (de- meaned and variance-normalized) data time series z(t) of length p are modelled as a mixture of q statistically indepen- dent unobserved source signals s(t) which are linearly mixed by A E lRPx'J and corrupted by additive noise v(t) such that z(t) = As(t) + av(t),