k_tJADE | R Documentation |
Computes the faster âkâ-version of tensorial JADE in an independent component model.
k_tJADE(x, k = NULL, maxiter = 100, eps = 1e-06)
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 |
It is assumed that S
is a tensor (array) of size p_1 \times p_2 \times \ldots \times p_r
with mutually independent elements and measured on N
units. The tensor independent component model further assumes that the tensors S are mixed from each mode
m
by the mixing matrix A_m
, m = 1, \ldots, r
, yielding the observed data X
. In R the sample of X
is saved as an array
of dimensions
p_1, p_2, \ldots, p_r, N
.
k_tJADE
recovers then based on x
the underlying independent components S
by estimating the r
unmixing matrices
W_1, \ldots, W_r
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 C^{ij}
for which |i - j| < k_m
.
If x
is a matrix, that is, r = 1
, the method reduces to JADE and the function calls k_JADE
.
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 |
Joni Virta
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), 6153â6157, \Sexpr[results=rd]{tools:::Rd_expr_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, \Sexpr[results=rd]{tools:::Rd_expr_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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/sjos.12445")}
k_JADE
, tJADE
, JADE
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))
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