CANDPARA {PTAk} | R Documentation |
Performs the identical models known as PARAFAC or CANDECOMP model.
CANDPARA(X,dim=3,test=1E-8,Maxiter=1000, smoothing=FALSE,smoo=list(NA), verbose=getOption("verbose"),file=NULL, modesnam=NULL,addedcomment="")
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 |
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.
a CANDPARA
(inherits from PTAk
) object
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.
Didier Leibovici c3s2i@free.fr
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.(related references in http://three-mode.leidenuniv.nl/)
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.