Modes or models: a critique on independent component analysis for fMRI.

are only uncorrelated). More importantly , ICA does this in a fashion that renders the expression of the components non-Gaussian. In the implementation proposed by McKeown et al. these distributions are super-Gaussian or 'sparse'. This simply means that things happen infrequently. Why is a 'sparse', or more generally a non-Gaussian, distribution interesting? The answer to this question is simple and extremely compelling: because measurements of biological systems receive contributions from many sources (e.g. dipoles generated by neuronal activity), the observations usually represent a [roughly linear] mixture of interesting things. By the central limit theorem this mixture conforms to a Gaussian distribution. As mixtures themselves are uninteresting the only interesting things must be non-Gaussian (assuming that Gaussian distributions arise only from mixing). This is the rather beautiful motivation behind ICA. There are many ways of understanding the nature of ICA but this perspective highlights why ICA is so pertinent to biological time-series. In what follows we will look at the particular implementation of ICA in relation to fMRI time-series proposed by McKeown et al. and then consider this contribution in the context of extant approaches to fMRI data analysis, and the larger issues it raises in terms of the scientific process in imaging neuroscience. ICA and fMRI time-series In application to multi-channel EEG or MEG signals, independent components are generally identified using correlations among channels that are estimated over time. The output comprises a set of non-orthogonal spatial modes whose dynamics are independent and have a sparse distribution. This decomposition can be viewed as an elegant 'un-mixing' of the observed (linearly mixed) time-series to reveal the underlying and independent biological sources. This is very sensible and appeals directly to the conceptual basis of ICA. However, this approach is not that used for fMRI. In fMRI there are many more voxels (i.e. channels) than there are scans (i.e. time points). This is the complement of the situation in EEG and poses a computationally intractable problem if one wanted to apply ICA to the correlations among voxels. The clever trick, adopted by McKeown et al., is literally to transpose the problem and derive independent components based upon correlations among different time points that are evaluated over voxels. The spatial modes that ensue are sparse and independent and express dynamics that are generally correlated. This lends the interpretation of the ensuing modes and their dynamics a very different complexion, relative to ICA analyses of …