# R/icajade.R In ica: Independent Component Analysis

```icajade <-
function(X, nc, center = TRUE, maxit = 100,
tol = 1e-6, Rmat = diag(nc)){
###### Joint Approximate Diagonalization of Eigenmatrices (JADE)
###### Nathaniel E. Helwig ([email protected])

### initial checks
X <- as.matrix(X)
nobs <- nrow(X)
nvar <- ncol(X)
nc <- as.integer(nc[1])
if(nc<1){ stop("Must set nc>=1 component.") }
maxit <- as.integer(maxit[1])
if(maxit<1){ stop("Must set maxit>=1 iteration.") }
tol <- tol[1]
if(tol<=0){ stop("Must set ctol>0.") }
if(nc>min(nobs,nvar)){ stop("Too many components. Set nc<=min(dim(X)).") }
if(nrow(Rmat)!=nc | ncol(Rmat)!=nc){ stop("Input 'Rmat' must be nc-by-nc rotation matrix.") }

### center and whiten
if(center) X <- scale(X,scale=FALSE)
xeig <- eigen(crossprod(X)/nobs,symmetric=TRUE)
nze <- sum(xeig\$val>xeig\$val[1]*.Machine\$double.eps)
if(nze<nc){
warning("Numerical rank of X is less than requested number of components (nc).\n  Number of components has been redefined as the numerical rank of X.")
nc <- nze
Rmat <- diag(nc)
}
Dmat <- sdiag(sqrt(xeig\$val[1:nc]))
Mprt <- tcrossprod(Dmat,xeig\$vec[,1:nc])
diag(Dmat) <- 1/diag(Dmat)
Pmat <- xeig\$vec[,1:nc]%*%Dmat
Xw <- X%*%Pmat   # whitened data

### check if nc=1
if(nc==1L){
return(list(S=Xw,M=Mprt,W=t(Pmat),Y=Xw,Q=t(Pmat),R=matrix(1),
vafs=(sum(Mprt^2)*nobs)/sum(X^2),iter=NA))
}

### basis eigenmatrices (using Jean-Francois Cardoso's symmetry trick)
ncstar <- nc*(nc+1)/2
idmat <- diag(nc)
emats <- matrix(0,nc,nc*ncstar)
crng <- 1:nc
for(i in 1:nc){
Xi <- Xw[,i]
Qij <- crossprod(matrix((Xi^2)/nobs,nobs,nc)*Xw,Xw) - idmat - 2*tcrossprod(idmat[,i],idmat[,i])
emats[,crng] <- Qij
crng <- crng + nc
if(i>1){
for(j in 1:(i-1)){
Xj <- Xw[,j]
Qij <- crossprod(matrix(Xi*Xj/nobs,nobs,nc)*Xw,Xw) - tcrossprod(idmat[,i],idmat[,j]) - tcrossprod(idmat[,j],idmat[,i])
emats[,crng] <- sqrt(2)*Qij
crng <- crng + nc
} # end if(i>1)
} # end for(j in 1:(i-1))
} # end for(i in 1:nc)

### iterative rotation
npairs <- nc*(nc-1)/2
thetas <- rep(1,npairs)
iter <- 0
vtol <- 1
while(vtol>tol && iter<maxit){
# sweep through angle pairs
for(p in 1:(nc-1)){
for(q in (p+1):nc){
# Givens angle
ip <- seq(p,nc*ncstar,by=nc)
iq <- seq(q,nc*ncstar,by=nc)
gp <- rbind(emats[p,ip]-emats[q,iq],emats[p,iq]+emats[q,ip])
gg <- tcrossprod(gp)
ton <- gg[1,1]-gg[2,2]
toff <- gg[1,2]+gg[2,1]
theta <- 0.5*atan2(toff,ton+sqrt(ton^2+toff^2))
thetas[nc*(p-1)-p*(p-1)/2+q-p] <- theta
# Givens rotation
cc <- cos(theta)
ss <- sin(theta)
gmat <- rbind(c(cc,-ss),c(ss,cc))
pair <- c(p,q)
Rmat[,pair] <- Rmat[,pair]%*%gmat
emats[pair,] <- crossprod(gmat,emats[pair,])
emats[,c(ip,iq)] <- cbind(cc*emats[,ip]+ss*emats[,iq],-ss*emats[,ip]+cc*emats[,iq])
}
}
# check for convergence
vtol <- max(abs(thetas))
iter <- iter + 1
} # end while(vtol>tol && iter<maxit)

### sort according to vafs
M <- crossprod(Rmat,Mprt)
vafs <- rowSums(M^2)
ix <- sort(vafs,decreasing=TRUE,index.return=TRUE)\$ix
M <- M[ix,]
Rmat <- Rmat[,ix]
vafs <- (vafs[ix]*nobs)/sum(X^2)

return(list(S=Xw%*%Rmat,M=t(M),W=t(Pmat%*%Rmat),Y=Xw,
Q=t(Pmat),R=Rmat,vafs=vafs,iter=iter))

}
```

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ica documentation built on May 24, 2018, 9:04 a.m.