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Figure 4:
Schematic illustration of the analysis steps involved in estimating
the PICA model.
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The individual steps that constitute the Probabilistic Independent Component
Analysis are illustrated in figure 4. The de-meaned
original data are first temporally pre-whitened using knowledge about
the noise
covariance
at each voxel location. The covariance of the data is
calculated from the data after normalization of the voxel-wise standard
deviation. In the case where spatial information is available, this is encoded
in the estimation of the sample covariance matrix
. This is used as
part of the probabilistic PCA steps to infer upon the unknown number of sources
contained in the data, which will provide us with an estimate of the noise and a
set of spatially whitened observations. We can re-estimate
from the
residuals and iterate the entire cycle. In practice, the output results do not
suggest a strong dependency on the form of
and preliminary results
suggest that it is sufficient to iterate these steps only
once. From the spatially whitened observations, the
individual component maps are estimated using the fixed point iteration scheme
(equation 13). These maps are separately transformed to scores
using the estimated standard deviation of the noise. In contrast to raw
IC estimates, the score maps depend on the amount of
variability explained by the entire decomposition at each voxel
location. Finally, Gaussian Mixture Models are fitted to the individual maps
in order to infer voxel locations that are significantly modulated by the
associated time course in order to allow for meaningful thresholding of the
images.
Next: Evaluation data
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Christian F. Beckmann
2003-08-05