Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
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Averaging of data, using time windows time-locked to repetitive stimuli, is a method that has long been used in Event-Related Potential (ERP) research. As event-related designs are becoming increasingly common in fMRI experiments, selective averaging is a natural approach to the analysis of these data sets. However, as the biophysical origin (and presumably the statistical properties) of the fMRI BOLD and ERP Signals fundamentally differ, there is a need to assess the implications of averaging raw fMRI data. We recorded a fMRI data series from a single subject performing a simple event-related task, consisting of 95 presentations of checkerboard visual stimuli. The data set was first dimension-reduced with Principal Component Analysis (PCA) and separated into 100 spatially independent components with Independent Component Analysis (ICA), an iterative technique whose weight matrix is normally initialized to the identity matrix. To determine components which were reproducible, and by inference represented deterministic features in the data, the ICA processing step was repeated, but this time initialized with the inverse of the weight matrix computed from the first analysis, a method supported by simulations. The mutual information between best-matching pairs of components each ICA analysis was plotted. Visual inspection suggested that 55 components were reproducible, accounting for 84% of the variance in the dimension-reduced data. The reproducible components exhibited much less trial-to-trial variability than the raw data from even the most activated voxels. Of the 55 reproducible components in the first series, the average responses of 28 independent components were significantly affected by stimulus presentation (p