fICA (version 1.1-3)

compute_alphas: Estimation of Alphas in the Asymptotic Covariance Matrix of the Deflation-based FastICA Estimator

Description

Using the estimates of the independent components, the function computes for a given set of nonlinearities, the quantities (alphas). Alphas determine the choices of the nonlinearities and in which order the nonlinearities are used in the adaptive deflation-based FastICA method.

Usage

compute_alphas(Z, gs=gf, dgs=dgf, name=gnames)

Value

A matrix where the ith row gives the estimates of alphas for the ith nonlinearity and the jth column corresponds to the jth component of Z.

Arguments

Z

a numeric matrix of the estimated independent components, which should be standardized so that the mean is zero and the covariance matrix is the identity matrix.

gs

a vector of functions containing the nonlinearities.

dgs

a vector of functions containing the first derivatives of the nonlinearities.

name

a vector of strings containing the names of the nonlinearities.

Author

Jari Miettinen

Details

See the references.

References

Hyvarinen, A. and Oja, E. (1997), A fast fixed-point algorithm for independent component analysis, Neural Computation, vol. 9, 1483--1492.

Nordhausen, K., Ilmonen, P., Mandal, A., Oja, H. and Ollila, E. (2011), Deflation-based FastICA reloaded, in Proc. "19th European Signal Processing Conference 2011 (EUSIPCO 2011)", Barcelona, 1854--1858.

Miettinen, J., Nordhausen, K., Oja, H. and Taskinen, S. (2014), Deflation-based FastICA with adaptive choices of nonlinearities, IEEE Transactions on Signal Processing, 62(21), 5716--5724.

See Also

fICA, nonlinearities, FOBI, k_JADE

Examples

A <- matrix(rnorm(9),3,3)
s1 <- rt(1000,6)
s2 <- rexp(1000,1)
s3 <- runif(1000)

S <- cbind(s1,s2,s3)
X <- S %*% t(A)

Sest <- fICA(X,method="def")$S

compute_alphas(Sest, gs=gf[1:3], dgs=dgf[1:3], name=gnames[1:3])