PCAn {PTAk}R Documentation

Principal Component Analysis on n modes

Description

Performs the Tuckern model using a space version of RPVSCC (SINGVA).

Usage

 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="")

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 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

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 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.

Value

a PCAn (inherits PTAk) object

Note

The use of metrics (diagonal or not) and smoothing extend flexibility of analysis.

Author(s)

Didier Leibovici didier@fmrib.ox.ac.uk

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.(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.


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