PCAn {PTAk} | R Documentation |
Performs the Tuckern model using a space version of RPVSCC (SINGVA
).
PCAn(X,dim=c(2,2,2,3),test=1E-12,Maxiter=400, 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 vector of numbers specifying the dimensions in each space |
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 rank of every bilinear form, 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 the 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 fetched at the www site quoted below.
a PCAn
(inherits PTAk
) object
The use of metrics (diagonal or not) and smoothing extend flexibility of analysis.
Didier Leibovici didier@fmrib.ox.ac.uk
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://www.fsw.leidenuniv.nl/~kroonenb/)
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.