Computes the tensorial principal components.
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x |
Numeric array of an order at least three. It is assumed that the last dimension corresponds to the sampling units. |
p |
A vector of the percentages of variation per each mode the principal components should explain. |
d |
A vector of the exact number of components retained per each mode. At most one of this and the previous argument should be supplied. |
The observed tensors (array) X of size p_1 x p_2 x ... x p_r measured on N units are projected from each mode on the eigenspaces of the m-mode covariance matrices of the corresponding modes. As in regular PCA, by retaining only some subsets of these projections (indices) with respective sizes d_1, d_2, ... d_r, a dimension reduction can be carried out, resulting into observations tensors of size d_1 x d_2 x ... x d_r. In R the sample of X is saved as an array
of dimensions
p_1, p_2, ..., p_r, N.
A list containing the following components:
S |
Array of the same size as x containing the principal components. |
U |
List containing the rotation matrices |
D |
List containing the amounts of variance explained by each index in each mode. |
p_comp |
The percentages of variation per each mode that the principal components explain. |
Xmu |
The data location. |
Joni Virta
Virta, J., Taskinen, S. and Nordhausen, K. (2016), Applying fully tensorial ICA to fMRI data, manuscript under preparation, ???, ???–???.
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