PTAk (version 1.2-6)

INITIA: 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

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).

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

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.

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