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sponding to the p largest eigenvalues, is transpose of Vp, and Xa is calculated from Eq. 10. Ap is a now smaller but full-rank matrix of eigenimages of Xa. The number p may be taken as the number of eigenvectors required to explain a predetermined proportion of the variance in the original data (e.g., >99%). ICA decomposition of the resulting eigenimages. Ap, gives,

Ca=WEAp, [13]

where Ca is the p by n matrix of component maps, and WE is the computed unmixing matrix.

Substituting for Ap from Eq. 11 gives:

[14]

or

[15]

whence

[16]

giving

[17]

since because eigenvectors are mutually orthogonal. Finding the p time courses (of length n) associated with each of the p maps can now be determined by examining the columns of the matrix,

[18]

The Heart and Stroke Foundation of Ontario, the Howard Hughes Medical Institute, and the Office of Naval Research supported this research.

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