Recovers independent sources by finding maximally non-Gaussian projections:
by the central limit theorem a mixture of independent sources is closer to
Gaussian than any source is. Two indeterminacies are intrinsic, not defects
– the SCALE of each source (absorbed into the mixing matrix, so components
are returned with unit variance) and their ORDER. Any comparison to known
sources must be up to permutation and sign. Gaussian sources cannot be
separated at all, since a rotation of independent Gaussians is again
independent Gaussian.
Usage
morie_esl_ica(
X,
k = NULL,
fun = "logcosh",
max_iter = 500L,
tol = 1e-08,
seed = 0L
)
Arguments
- X
Observed mixtures, n by p.
- k
Number of components; defaults to p.
- fun
Contrast: "logcosh", "exp" or "cube".
- max_iter, tol
Fixed-point controls.
- seed
Seed for the random initialisation.
Value
List with sources (unit variance), unmixing, mixing,
whitening, mean, n_iter, converged.
References
Hyvarinen, A., & Oja, E. (2000). Independent component analysis:
Algorithms and applications. Neural Networks 13(4-5), 411-430.
Examples
if (requireNamespace("ranger", quietly = TRUE)) {
tt <- seq(0, 8 * pi, length.out = 500)
S <- cbind(sin(tt), sign(cos(2.7 * tt)))
A <- matrix(c(1, -0.6, 0.7, 1.2), 2)
r <- morie_esl_ica(S %*% t(A), k = 2, seed = 1L)
round(apply(r$sources, 2, function(z) sqrt(mean((z - mean(z))^2))), 6)
}
#> [1] 1 1
