k_tJADE {tensorBSS} | R Documentation |
k-tJADE for Tensor-Valued Observations
Description
Computes the faster “k”-version of tensorial JADE in an independent component model.
Usage
k_tJADE(x, k = NULL, maxiter = 100, eps = 1e-06)
Arguments
x |
Numeric array of an order at least two. It is assumed that the last dimension corresponds to the sampling units. |
k |
A vector with one less element than dimensions in |
maxiter |
Maximum number of iterations. Passed on to |
eps |
Convergence tolerance. Passed on to |
Details
It is assumed that is a tensor (array) of size
with mutually independent elements and measured on
units. The tensor independent component model further assumes that the tensors S are mixed from each mode
by the mixing matrix
,
, yielding the observed data
. In R the sample of
is saved as an
array
of dimensions
.
k_tJADE
recovers then based on x
the underlying independent components by estimating the
unmixing matrices
using fourth joint moments at the same time in a more efficient way than
tFOBI
but also in fewer numbers than tJADE
. k_tJADE
diagonalizes in each mode only those cumulant matrices for which
.
If x
is a matrix, that is, , the method reduces to JADE and the function calls
k_JADE
.
Value
A list with class 'tbss', inheriting from class 'bss', containing the following components:
S |
Array of the same size as x containing the independent components. |
W |
List containing all the unmixing matrices |
Xmu |
The data location. |
k |
The used vector of |
datatype |
Character string with value "iid". Relevant for |
Author(s)
Joni Virta
References
Miettinen, J., Nordhausen, K., Oja, H. and Taskinen, S. (2013), Fast Equivariant JADE, In the Proceedings of 38th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2013), 6153–6157, doi: 10.1109/ICASSP.2013.6638847
Virta J., Li B., Nordhausen K., Oja H. (2018): JADE for tensor-valued observations, Journal of Computational and Graphical Statistics, 27, 628-637, doi: 10.1080/10618600.2017.1407324
Virta J., Lietzen N., Ilmonen P., Nordhausen K. (2021): Fast tensorial JADE, Scandinavian Journal of Statistics, 48, 164-187, doi: 10.1111/sjos.12445
See Also
Examples
n <- 1000
S <- t(cbind(rexp(n)-1,
rnorm(n),
runif(n, -sqrt(3), sqrt(3)),
rt(n,5)*sqrt(0.6),
(rchisq(n,1)-1)/sqrt(2),
(rchisq(n,2)-2)/sqrt(4)))
dim(S) <- c(3, 2, n)
A1 <- matrix(rnorm(9), 3, 3)
A2 <- matrix(rnorm(4), 2, 2)
X <- tensorTransform(S, A1, 1)
X <- tensorTransform(X, A2, 2)
k_tjade <- k_tJADE(X)
MD(k_tjade$W[[1]], A1)
MD(k_tjade$W[[2]], A2)
tMD(k_tjade$W, list(A1, A2))
k_tjade <- k_tJADE(X, k = c(2, 1))
MD(k_tjade$W[[1]], A1)
MD(k_tjade$W[[2]], A2)
tMD(k_tjade$W, list(A1, A2))