mpca {rTensor}

Multilinear Principal Components Analysis

Description

This is basically the Tucker decomposition of a K-Tensor, tucker, with one of the modes uncompressed. If K = 3, then this is also known as the Generalized Low Rank Approximation of Matrices (GLRAM). This implementation assumes that the last mode is the measurement mode and hence uncompressed. This is an iterative algorithm, with two possible stopping conditions: either relative error in Frobenius norm has gotten below tol, or the max_iter number of iterations has been reached. For more details on the MPCA of tensors, consult Lu et al. (2008).

Usage

mpca(tnsr, ranks = NULL, max_iter = 25, tol = 1e-05)

Arguments

tnsr

Tensor with K modes

ranks

a vector of the compressed modes of the output core Tensor, this has length K-1

max_iter

maximum number of iterations if error stays above tol

tol

relative Frobenius norm error tolerance

Details

Uses the Alternating Least Squares (ALS) estimation procedure. A progress bar is included to help monitor operations on large tensors.

Value

a list containing the following:

Z_ext

the extended core tensor, with the first K-1 modes given by ranks

U

a list of K-1 orthgonal factor matrices - one for each compressed mode, with the number of columns of the matrices given by ranks

conv

whether or not resid < tol by the last iteration

est

estimate of tnsr after compression

norm_percent

the percent of Frobenius norm explained by the approximation

fnorm_resid

the Frobenius norm of the error fnorm(est-tnsr)

all_resids

vector containing the Frobenius norm of error for all the iterations

Note

The length of ranks must match tnsr@num_modes-1.

References

H. Lu, K. Plataniotis, A. Venetsanopoulos, "Mpca: Multilinear principal component analysis of tensor objects". IEEE Trans. Neural networks, 2008.

See Also

tucker, hosvd

Examples

### How to retrieve faces_tnsr from figshare
# faces_tnsr <- load_orl()
# subject <- faces_tnsr[,,21,]
dummy_faces_tnsr <- rand_tensor(c(92,112,40,10))
subject <- dummy_faces_tnsr[,,21,]
mpcaD <- mpca(subject, ranks=c(10, 10))
mpcaD$conv
mpcaD$norm_percent
plot(mpcaD$all_resids)