tPCA: PCA for Tensor-Valued Observations
In tensorBSS: Blind Source Separation Methods for Tensor-Valued Observations

Description Usage Arguments Details Value Author(s) References Examples

View source: R/tPCA.R

Computes the tensorial principal components.

1	tPCA(x, p = NULL, d = NULL)

`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, ???, ???–???.

# Digit data example

library(ElemStatLearn)
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)