compute_alphas {fICA}

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)

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.

Details

See the references.

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.

Author(s)

Jari Miettinen

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])