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ICA can be summarised as follows:
- Find the PCA decomposition of the data :
where
with
being the SVD.
- Reduce the dimensionality by selecting the largest components of the PCA (thresholding the power - given by ), giving .
- Find the orthogonal matrix such that is minimised where
. The function needs to measure
statistical dependence of the rows of (e.g. Negentropy).
- The resulting rows of the matrix are the ICs (spatial maps) which are orthonormal and the columns of the matrix
are the associated time courses in the original data space (which are not orthogonal in general, although in the reduced data space the columns of are orthogonal).
Stephen Smith
2001-11-29