CANDPARA {PTAk}

CANonical DECOMPosition analysis and PARAllel FACtor analysis

Description

Performs the identical models known as PARAFAC or CANDECOMP model.

Usage

CANDPARA(X,dim=3,test=1E-8,Maxiter=1000,
                     smoothing=FALSE,smoo=list(NA),
                      verbose=getOption("verbose"),file=NULL,
                       modesnam=NULL,addedcomment="")

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.

dim

a number specifying the number of rank-one tensors

test

control of convergence

Maxiter

maximum number of iterations allowed for convergence

smoothing

see SVDgen

smoo

see PTA3

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"

addedcomment

character string printed after the title of the analysis

Details

Looking for the best rank-one tensor approximation (LS) the three methods described in the package are equivalent. If the number of tensors looked for is greater then one the methods differs: PTA-kmodes will look for best approximation according to the orthogonal rank (i.e. the rank-one tensors are orthogonal), PCA-kmodes will look for best approximation according to the space ranks (i.e. the ranks of all (simple) bilinear forms , that is the number of components in each space), PARAFAC/CANDECOMP will look for best approximation according to the rank (i.e. the rank-one tensors are not necessarily orthogonal). For sake of comparisons the PARAFAC/CANDECOMP method and the PCA-nmodes are also in the package but complete functionnality of the use these methods and more complete packages may be checked at the www site quoted below.

Value

a CANDPARA (inherits from PTAk) object

Note

The use of metrics (diagonal or not) and smoothing extends flexibility of analysis. This program runs slow! A PARAFAC orthogonal can be done with PTAk looking only for k-modes Principal Tensors i.e. with the options nbPT=c(rep(0,k-2),dim), nbPT2=0. It is identical to look in any PTAk decomposition only for the kmodes solution but obviously with unecessary computations.

Author(s)

Didier G. Leibovici

References

Caroll J.D and Chang J.J (1970) Analysis of individual differences in multidimensional scaling via n-way generalization of 'Eckart-Young' decomposition. Psychometrika 35,283-319.

Harshman R.A (1970) Foundations of the PARAFAC procedure: models and conditions for 'an explanatory' multi-mode factor analysis. UCLA Working Papers in Phonetics, 16,1-84.

Kroonenberg P (1983) Three-mode Principal Component Analysis: Theory and Applications. DSWO press. Leiden.)

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.