G1 {ProDenICA}

FastICA contrast functions.

Description

contrast functions for computing the negentropy criteria used in FastICA; see references.

Usage

G1(s, a=1)
G0(s, a=1)

Arguments

s

estimated independent component

a

additional tuning parameter (only used in G1)

Value

a list with components

Gs

contrast function evaluated at values of x. mean(Gs) is measure of negentropy.

gs

estimated first derivative of Gs at x

gps

estimated second derivative of Gs at x

Author(s)

Trevor Hastie and Rob Tibshirani

References

Hyvarinen, A., Karhunen, J. and Oja, E. (2001). Independent Component Analysis, Wiley, New York
Hastie, T. and Tibshirani, R. (2003) Independent Component Analysis through Product Density Estimation in Advances in Neural Information Processing Systems 15 (Becker, S. and Obermayer, K., eds), MIT Press, Cambridge, MA. pp 649-656
Hastie, T., Tibshirani, R. and Friedman, J. (2009) Elements of Statistical Learning (2nd edition), Springer.
https://hastie.su.domains/ElemStatLearn/printings/ESLII_print12_toc.pdf

See Also

GPois and ProDenICA

Examples

p=2
### Can use letters a-r below for dist
dist="n" 
N=1024
A0<-mixmat(p)
s<-scale(cbind(rjordan(dist,N),rjordan(dist,N)))
x <- s %*% A0
fit=ProDenICA(x,Gfunc=G1, whiten=TRUE)