INITIA {PTAk} | R Documentation |
Gives the first Tucker1 components of a given tensor.
INITIA(X,modesnam=NULL,method="Presvd",dim=1,...)
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). |
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
.
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 |
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.
Didier Leibovici c3s2i@free.fr
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.