steadyICA (version 1.0)

rightskew: force ICs to have positive skewness and order by skewness

Description

The ICA model is only identifiable up to signed permutations. This function provides a canonical ordering for ICA that is useful for fMRI or studies where signals are skewed. Multiplies columns of S that are left-skewed by -1 to force right skewness. Optionally orders the columns by descending skewness.

Usage

rightskew(S, M = NULL, order.skew = TRUE)

Arguments

S

n x d matrix

M

d x p mixing matrix

order.skew

Option to return the permutation of columns of S from largest to smallest skewness. Also returns a permuted version of M that corresponds with the permuted S.

Value

• Returns the matrix S such that all columns have positive skewness. If optional argument M is supplied, returns a list with the new S and corresponding M.

References

Eloyan, A. & Ghosh, S. A Semiparametric Approach to Source Separation using Independent Component Analysis Computational Statistics and Data Analysis, 2013, 58, 383 - 396.

Examples

nObs = 1024
simS<-cbind(rgamma(nObs, shape = 1, scale = 2),
            rgamma(nObs, shape = 9, scale = 0.5),
            -1*rgamma(nObs, shape = 3, scale = 2))

apply(simS,2,function(x){ 
  (sum((x - mean(x))^3)/length(x))/(sum((x - mean(x))^2)/length(x))^(3/2)})

canonicalS <- rightskew(simS)

apply(canonicalS,2,function(x){
 (sum((x - mean(x))^3)/length(x))/(sum((x - mean(x))^2)/length(x))^(3/2)})