Independent component analysis for brain fMRI does not select for independence

Abstract

InfoMax and FastICA are the independent component analysis algorithms most used and apparently most effective for brain fMRI. We show that this is linked to their ability to handle effectively sparse components rather than independent components as such. The mathematical design of better analysis tools for brain fMRI should thus emphasize other mathematical characteristics than independence.I ndependent component analysis (ICA), a framework for separating a mixture of different components into its constituents, has been proposed for many applications, including functional magnetic resonance imaging (fMRI) (1-3). Separating a signal mixture into its components is impossible in general; however, many cases of interest allow for special underlying assumptions that make the problem tractable. ICA algorithms decompose into a sum of signals that "optimize independence." Several algorithms and software packages are available for ICA (4, 5).The first blind source separation in fMRI via ICA used InfoMax (1); other ICA algorithms for fMRI followed, such as FastICA (2, 5). These algorithms work well if the components have "generalized Gaussian" distributions of the form p(x) = Cexp(−α|x| γ ), with γ = 2. More general ICA algorithms that assume less about the components can separate into independent components mixtures for which Infomax and FastICA fail. Nevertheless, these 2 are the most used ICA algorithms for brain fMRI.Stochastic processes are independent if the distribution of either remains the same if the other is conditioned to any subregion of their range. Detecting deviations from independence requires large samples. In fMRI experiments, brain activity is measured in small volumetric regions or voxels v ∈ V , at times t n , n = 1, . . . , N.(fMRI measures brain function via the associated increase of oxygen-enriched blood flow. The hemodynamic response function is the flow's time profile for 1 pulse in brain activity; from a signal analysis point of view, it blurs the signal in time.) Often the voxels outnumber N by far. Thus, one often prefers to view the voxel-index v as labeling the samples over which independence is sought (spatial ICA, or SICA), rather than the t n (temporal ICA, or TICA).In the linear model for brain activation (6), the total brain activity X (t, v) is assumed to be a linear superposition of the different ongoing brain activity patterns:, where the C correspond to the brain activity patterns, and the "mixing matrix" M gives the corresponding time courses. At high signal amplitudes, saturation effects "spoil" linearity; nevertheless, the linear model is remarkably effective. We shall stick to it here.Typically, the brain function under study is turned "off" and "on" by having subjects perform a task during defined periods, punctuated by either resting states or other tasks. The activation map of interest C act (v) associated with a time course M act (t) related to the task paradigm, is then identified via a statistical analysis. When a strict paradigm is not possible, or to capture more compl...

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