INITIA {PTAk}

Initialisation used in SINGVA

Description

Gives the first Tucker1 components of a given tensor.

Usage

   INITIA(X,modesnam=NULL,method="svds",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. The method method="svds" performs alike method="svd" but on a sum of tables instead of the Tucker1 approach.

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 G. Leibovici

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