tMD: Minimum Distance Index of a Kronecker Product
In tensorBSS: Blind Source Separation Methods for Tensor-Valued Observations

Description Usage Arguments Details Value Author(s) References See Also Examples

A shortcut function for computing the minimum distance index of a tensorial ICA estimate on the Kronecker product “scale” (the vectorized space).

1	tMD(W.hat, A)

`W.hat`	A list of `r` unmixing matrix estimates, W_1, W_2, ..., W_r.
`A`	A list of `r` mixing matrices, A_1, A_2, ..., A_r.

The function computes the minimum distance index between W.hat[[r]] %x% ... %x% W.hat[[1]] and A[[r]] %x% ... %x% A[[1]]. The index is useful for comparing the performance of a tensor-valued ICA method to that of a method using first vectorization and then some vector-valued ICA method.

The value of the MD index of the Kronecker product.

Joni Virta

Ilmonen, P., Nordhausen, K., Oja, H. and Ollila, E. (2010), A New Performance Index for ICA: Properties, Computation and Asymptotic Analysis. In Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R. and Vincent, E. (editors) Latent Variable Analysis and Signal Separation, 229-236, Springer.

Virta, J., Li, B., Nordhausen, K. and Oja, H., (2017), Independent component analysis for tensor-valued data, Journal of Multivariate Analysis, doi: 10.1016/j.jmva.2017.09.008

MD

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)

tfobi <- tFOBI(X)

MD(tfobi$W[[2]] %x% tfobi$W[[1]], A2 %x% A1)
tMD(list(tfobi$W[[2]]), list(A2))