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#############################################################################################################
# Authors:
# The function ica.par and ica.def are borrowed from the fastICA package (see references in help file).
#
# created: 2011
# last modified: 2011
#
# Copyright (C) 2011
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
#############################################################################################################
ica.def <-
function (X, ncomp, tol, fun, alpha, max.iter, verbose, w.init)
{
n <- nrow(X)
p <- ncol(X)
W <- matrix(0, ncomp, ncomp)
for (i in 1:ncomp) {
w <- matrix(w.init[i,], ncomp, 1)
if (i > 1) {
t <- w
t[1:length(t)] <- 0
for (u in 1:(i - 1)) {
k <- sum(w * W[u, ])
t <- t + k * W[u, ]
}
w <- w - t
}
w <- w/sqrt(sum(w^2))
lim <- rep(1000, max.iter)
it <- 1
if (fun == "logcosh") {
while (lim[it] > tol && it < max.iter) {
wx <- t(w) %*% X
gwx <- tanh(alpha * wx)
gwx <- matrix(gwx, ncomp, p, byrow = TRUE)
xgwx <- X * gwx
v1 <- apply(xgwx, 1, FUN = mean)
g.wx <- alpha * (1 - (tanh(alpha * wx))^2)
v2 <- mean(g.wx) * w
w1 <- v1 - v2
w1 <- matrix(w1, ncomp, 1)
it <- it + 1
if (i > 1) {
t <- w1
t[1:length(t)] <- 0
for (u in 1:(i - 1)) {
k <- sum(w1 * W[u, ])
t <- t + k * W[u, ]
}
w1 <- w1 - t
}
w1 <- w1/sqrt(sum(w1^2))
lim[it] <- Mod(Mod(sum((w1 * w))) - 1)
w <- matrix(w1, ncomp, 1)
}
}
if (fun == "exp") {
while (lim[it] > tol && it < max.iter) {
wx <- t(w) %*% X
gwx <- wx * exp(-(wx^2)/2)
gwx <- matrix(gwx, ncomp, p, byrow = TRUE)
xgwx <- X * gwx
v1 <- apply(xgwx, 1, FUN = mean)
g.wx <- (1 - wx^2) * exp(-(wx^2)/2)
v2 <- mean(g.wx) * w
w1 <- v1 - v2
w1 <- matrix(w1, ncomp, 1)
it <- it + 1
if (i > 1) {
t <- w1
t[1:length(t)] <- 0
for (u in 1:(i - 1)) {
k <- sum(w1 * W[u, ])
t <- t + k * W[u, ]
}
w1 <- w1 - t
}
w1 <- w1/sqrt(sum(w1^2))
lim[it] <- Mod(Mod(sum((w1 * w))) - 1)
if (verbose)
message("Iteration ", it - 1, " tol = ", format(lim[it]))
w <- matrix(w1, ncomp, 1)
}
}
W[i, ] <- w
}
return(W)
}
ica.par <- function (X, ncomp, tol, fun, alpha, max.iter, verbose, w.init)
{
Diag <- function(d) if(length(d) > 1L) diag(d) else as.matrix(d)
n <- nrow(X)
p <- ncol(X)
W <- w.init+matrix(c(1:9),ncomp,ncomp)
sW <- La.svd(W)
W <- sW$u %*% Diag(1/sW$d) %*% t(sW$u) %*% W
W1 <- W
lim <- rep(1000, max.iter)
it <- 1
if (fun == "logcosh") {
while (lim[it] > tol && it < max.iter) {
wx <- W %*% X
gwx <- tanh(alpha * wx)
v1 <- gwx %*% t(X)/p
g.wx <- alpha * (1 - (gwx)^2)
v2 <- Diag(apply(g.wx, 1, FUN = mean)) %*% W
W1 <- v1 - v2
sW1 <- La.svd(W1)
W1 <- sW1$u %*% Diag(1/sW1$d) %*% t(sW1$u) %*% W1
lim[it + 1] <- max(Mod(Mod(diag(W1 %*% t(W))) - 1))
W <- W1
if (verbose)
message("Iteration ", it, " tol = ", format(lim[it + 1]))
it <- it + 1
}
}
if (fun == "exp") {
while (lim[it] > tol && it < max.iter) {
wx <- W %*% X
gwx <- wx * exp(-(wx^2)/2)
v1 <- gwx %*% t(X)/p
g.wx <- (1 - wx^2) * exp(-(wx^2)/2)
v2 <- Diag(apply(g.wx, 1, FUN = mean)) %*% W
W1 <- v1 - v2
sW1 <- La.svd(W1)
W1 <- sW1$u %*% Diag(1/sW1$d) %*% t(sW1$u) %*% W1
lim[it + 1] <- max(Mod(Mod(diag(W1 %*% t(W))) - 1))
W <- W1
if (verbose)
message("Iteration ", it, " tol = ", format(lim[it + 1]))
it <- it + 1
}
}
return(W)
}
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