INITIA {PTAk}R Documentation

Initialisation used in SINGVA

Description

Gives the first Tucker1 components of a given tensor.

Usage

   INITIA(X,modesnam=NULL,method="Presvd",dim=1,...)

Arguments

X a tensor (as an array) of order k
modesnam a character vector of the names of the modes
method uses either the inbuilt SVD method="svd" or a power algorithm giving only the first method="Presvd" or any other function given applying to the column space of a matrix and returning a list with v (in columns vectors as in svd) and d.
dim default 1 in each space otherwise specify the number of dimensions e.g. c(2,3..,2) (with "Presvd" dim is obviously 1)
...

{extra arguments of the method method: the first argument is fixed (see details). }

Details

Computes the first (or dim) right singular vector (or other summaries) for every representation of the tensor as a matrix with dim(X)[i] columns, i=1...k.

Value

a list (of length k) of lists with arguments:

v the singular vectors in rows
modesnam a character object naming the mode, "m i" otherwise
n labels of mode i entries as given in dimnames of the data, can be NULL
d the corresponding first singular values

Note

The collection these eigenvectors, is known as the Tucker1 solution or initialisation related to PCA-3modes or PCA-nmodes models. If a function is given it may include dim as argument.

Author(s)

Didier Leibovici c3s2i@free.fr

References

Kroonenberg P.M (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.

See Also

SINGVA, PTAk


[Package PTAk version 1.1-15 Index]