matchICA {steadyICA}

match independent components using the Hungarian method

Description

The ICA model is only identifiable up to signed permutations of the ICs. This function finds the signed permutation of a matrix S such that ||S%*%P - template|| is minimized. Optionally also matches the mixing matrix M.

Usage

matchICA(S, template, M = NULL)

Arguments

S

the n x d matrix of ICs to be matched

template

the n x d matrix that S is matched to.

M

an optional d x p mixing matrix corresponding to S that will also be matched to the template

Value

Returns the signed permutation of S that is matched to the template. If the optional argument M is provided, returns a list with the permuted S and M matrices.

Author(s)

Benjamin Risk

References

Kuhn, H. The Hungarian Method for the assignment problem Naval Research Logistics Quarterly, 1955, 2, 83 - 97

Risk, B.B., D.S. Matteson, D. Ruppert, A. Eloyan, B.S. Caffo. In review, 2013. Evaluating ICA methods with an application to resting state fMRI.

See Also

frobICA clue::solve_LSAP

Examples

set.seed(999)
nObs <- 1024
nComp <- 3
# simulate from some gamma distributions:
simS<-cbind(rgamma(nObs, shape = 1, scale = 2),
            rgamma(nObs, shape = 3, scale = 2),
            rgamma(nObs, shape = 9, scale = 0.5))

simM <- matrix(rnorm(9),3)
pMat <- matrix(c(0,-1,0,1,0,0,0,0,-1),3)
permS <- simS%*%pMat
permM <- t(pMat)%*%simM

matchedS <- matchICA(S = permS, template = simS, M = permM)
sum(abs(matchedS$S - simS))
sum(abs(simM - matchedS$M))