tPCA {tensorBSS} | R Documentation |
PCA for Tensor-Valued Observations
Description
Computes the tensorial principal components.
Usage
tPCA(x, p = NULL, d = NULL)
Arguments
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. |
Details
The observed tensors (array) X
of size p_1 \times p_2 \times \ldots \times 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 \times d_2 \times \ldots \times d_r
. In R the sample of X
is saved as an array
of dimensions
p_1, p_2, \ldots, p_r, N
.
Value
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. |
Author(s)
Joni Virta
References
Virta, J., Taskinen, S. and Nordhausen, K. (2016), Applying fully tensorial ICA to fMRI data, Signal Processing in Medicine and Biology Symposium (SPMB), 2016 IEEE,
doi: 10.1109/SPMB.2016.7846858
Examples
# Digit data example
data(zip.train)
x <- zip.train
rows <- which(x[, 1] == 0 | x[, 1] == 1)
x0 <- x[rows, 2:257]
y0 <- x[rows, 1] + 1
x0 <- t(x0)
dim(x0) <- c(16, 16, 2199)
tpca <- tPCA(x0, d = c(2, 2))
pairs(t(apply(tpca$S, 3, c)), col=y0)