Analysis was carried out using Probabilistic Independent Component Analysis [Beckmann 2004] as implemented in MELODIC (Multivariate Exploratory Linear Decomposition into Independent Components) Version 3.10, part of FSL (FMRIB's Software Library, www.fmrib.ox.ac.uk/fsl).
The following data pre-processing was applied to the input data: masking of non-brain voxels; voxel-wise de-meaning of the data; normalisation of the voxel-wise variance;
Pre-processed data were whitened and projected into a 19-dimensional subspace using probabilistic Principal Component Analysis where the number of dimensions was estimated using the Laplace approximation to the Bayesian evidence of the model order [Minka 2000, Beckmann 2004].
The whitened observations were decomposed into sets of vectors which describe signal variation across the temporal domain (time-courses), the session/subject domain and across the spatial domain (maps) by optimising for non-Gaussian spatial source distributions using a fixed-point iteration technique [Hyvärinen 1999]. Estimated Component maps were divided by the standard deviation of the residual noise and thresholded by fitting a mixture model to the histogram of intensity values [Beckmann 2004].
[Hyvärinen 1999] A. Hyvärinen. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 10(3):626-634, 1999.
[Beckmann 2004] C.F. Beckmann and S.M. Smith. Probabilistic Independent Component Analysis for Functional Magnetic Resonance Imaging. IEEE Transactions on Medical Imaging 23(2):137-152 2004.
[Beckmann 2005] C.F. Beckmann and S.M. Smith. Tensorial extensions of independent component analysis for multisubject FMRI analysis. Neuroimage 25(1):294-311 2005.
[Everson 2000] R. Everson and S. Roberts. Inferring the eigenvalues of covariance matrices from limited, noisy data. IEEE Trans Signal Processing, 48(7):2083-2091, 2000
[Tipping 1999] M.E. Tipping and C.M.Bishop. Probabilistic Principal component analysis. J Royal Statistical Society B, 61(3), 1999.
[Beckmann 2001] C.F. Beckmann, J.A. Noble and S.M. Smith. Investigating the intrinsic dimensionality of FMRI data for ICA. In Seventh Int. Conf. on Functional Mapping of the Human Brain, 2001.
[Minka 2000] T. Minka. Automatic choice of dimensionality for PCA. Technical Report 514, MIT Media Lab Vision and Modeling Group, 2000.