Gives the first Tucker1 components of a given tensor.
INITIA(X,modesnam=NULL,method="svds",dim=1,...)a list (of length k) of lists with arguments:
the singular vectors in rows
a character object naming the mode, "m i" otherwise
labels of mode i entries as given in dimnames of the data, can be NULL
the corresponding first singular values
a tensor (as an array) of order k
a character vector of the names of the modes
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.
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).
Didier G. Leibovici
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.
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.
SINGVA, PTAk