APSOLUk {PTAk}

Associated k-modes Principal Tensors of a k-modes Principal Tensor

Description

Computes all the (k-1)-modes associated solutions to the given Principal Tensor of the given tensor. Calls recursively PTAk.

Usage

 APSOLUk(X,solu,nbPT,nbPT2=1,
                       smoothing=FALSE,smoo=list(NA),
                        minpct=0.1,ptk=NULL,
                         verbose=getOption("verbose"),file=NULL,
                          modesnam=NULL, ...)

Arguments

X

a tensor (as an array) of order k, if non-identity metrics are used X is a list with data as the array and met a list of metrics

solu

a PTAk object

nbPT

a number or a vector of dimension (k-2)

nbPT2

integer, if 0 no 2-modes solutions will be computed, 1 means all, >1 otherwise

smoothing

see SVDgen

smoo

see PTA3

minpct

numerical 0-100 to control of computation of future solutions at this level and below

ptk

a number identifying in solutions the Principal Tensor to use or the last (if NULL)

verbose

control printing

file

output printed at the prompt if NULL, or printed in the given ‘file’

modesnam

character vector of the names of the modes, if NULL "mo 1" ..."mo k"

...

any other arguments passed to PTAk or other functions

Details

For each component of the identified Principal Tensor given in solutions, a PTA-(k-1)modes of the contracted product of X and the component is done. This gives all the associated Principal Tensors which updates solutions supposed to contain a Principal Tensors of X at the first place. For full description of arguments see PTAk.

Value

an updated PTAk object

Note

Usually (i.e. as in PTA3 and PTAk) the principal tensor used is the first Principal Tensor of X (and is the last updated in solutions). If it is another Principal Tensor, the obtained associated solutions do not stricto sensu refer to the SVD-kmodes decomposition (because the orthogonality is defined in the whole tensor space not necessarily on each component space) but are still meaningful. This function is usually called by PTAk but can be used on its own to carry on a PTAk analysis if X is the projected (of the original data) on the orthogonal of all the kmodes Principal Tensor. In other words the ptk rank-one tensor in solutions should be the first best rank-one tensor approximating X for this decomposition analysis to be called PTA-kmodes.

Author(s)

Didier G. Leibovici

References

Leibovici D and Sabatier R (1998) A Singular Value Decomposition of a k-ways array for a Principal Component Analysis of multi-way data, the PTA-k. Linear Algebra and its Applications, 269:307-329.

See Also

PTAk