proc_align3 {fase}

Procrustes alignment for 3-mode tensors

Description

proc_align3 applies one orthogonal transformation to the columns of each of the n \times d slices of an n \times d \times m array A to find the best approximation (in terms of matrix Frobenius norm, averaged over the n \times d slices) to a second n \times d \times m array B. Optionally, it may also return the optimal transformation matrix.

Usage

proc_align3(A,B,return_orth=FALSE)

Arguments

A

An n \times d \times m array.

B

An n \times d \times m array.

return_orth

A Boolean which specifies whether to return the orthogonal transformation. Defaults to FALSE.

Value

If return_orth is FALSE, returns the n \times d \times m array resulting from applying the optimal aligning transformation to the columns of the n \times d slices of A. Otherwise, returns a list with two entries:

Ao

The n \times d matrix resulting from applying the optimal aligning transformation to the columns of the n \times d slices of A.

orth

The d \times d optimal aligning orthogonal transformation matrix.