Part B: Resting state fMRI visualization, multidimensional arrays and independent component analysis (ICA). Generating Report

.Rhistory

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+alpha.LM
+alpha.ML
+degree(g)
+sort(degree(g))
+sort(degree(g),decreasing=FALSE)
+sort(degree(g),decreasing=F)
+sort(degree(g),decreasing=false)
+sort(degree(g), decreasing = TRUE)
+head(sort(degree(g), decreasing = TRUE))
+stddev(degree(g))
+sd(degree(g))
+tail(sort(degree(g), decreasing = TRUE))
+plot(log(g.breaks.clean), log(g.probs.clean))
+# Homework 4 for the University of Tulsa' s CS-7863 Network Theory Course
+# Degree Distribution
+# Professor: Dr. McKinney, Spring 2022
+# Noah Schrick - 1492657
+library(igraph)
+library(igraphdata)
+data(yeast)
+g <- yeast
+g.netname <- "Yeast"
+################# Set up Work #################
+g.vec <- degree(g)
+g.hist <- hist(g.vec, freq=FALSE, main=paste("Histogram of the", g.netname,
+" Network"))
+legend("topright", c("Guess", "Poisson", "Least-Squares Fit",
+"Max Log-Likelihood"), lty=c(1,2,3,4), col=c("#40B0A6",
+"#006CD1", "#E66100", "#D35FB7"))
+g.mean <- mean(g.vec)
+g.seq <- 0:max(g.vec) # x-axis
+################# Guessing Alpha #################
+alpha.guess <- 1.5
+lines(g.seq, g.seq^(-alpha.guess), col="#40B0A6", lty=1, lwd=3)
+################# Poisson #################
+g.pois <- dpois(g.seq, g.mean, log=F)
+lines(g.seq, g.pois, col="#006CD1", lty=2, lwd=3)
+################# Linear model: Least-Squares Fit #################
+g.breaks <- g.hist$breaks[-c(1)] # remove 0
+g.probs <- g.hist$density[-1] # make lengths match
+# Need to clean up probabilities that are 0
+nz.probs.mask <- g.probs!=0
+g.breaks.clean <- g.breaks[nz.probs.mask]
+g.probs.clean <- g.probs[nz.probs.mask]
+plot(log(g.breaks.clean), log(g.probs.clean))
+g.fit <- lm(log(g.probs.clean)~log(g.breaks.clean))
+summary(g.fit)
+alpha.LM <- coef(g.fit)[2]
+lines(g.seq, g.seq^(-alpha.LM), col="#E66100", lty=3, lwd=3)
+################# Max-Log-Likelihood #################
+n <- length(g.breaks.clean)
+kmin <- g.breaks.clean[1]
+alpha.ML <- 1 + n/sum(log(g.breaks.clean/kmin))
+alpha.ML
+lines(g.seq, g.seq^(-alpha.ML), col="#D35FB7", lty=4, lwd=3)
+plot(log(g.breaks.clean), log(g.probs.clean))
+g.breaks.clean <- g.breaks[nz.probs.mask]
+g.probs.clean <- g.probs[nz.probs.mask]
+plot(log(g.breaks.clean), log(g.probs.clean))
+BiocManager::install()
+simDats <- createSimulation2(data.type = "discrete", avg.maf = 0.2, sim.type = "mainEffect",
+pct.train = 0.5, pct.holdout = 0.5, pct.validation = 0,
+main.bias = 0.4, pct.signals = 0.2)
+# npdro::createSimulation2() example for gwas simulation
+library(npdro)
+# npdro::createSimulation2() example for gwas simulation
+if (!require("npdro")) install.packages("npdro")
+library(npdro)
+# npdro::createSimulation2() example for gwas simulation
+install_github("insilico/npdro")
+# npdro::createSimulation2() example for gwas simulation
+if (!require("devtools")) install.packages("devtools")
+library(devtools)
+install_github("insilico/npdro")
+# npdro::createSimulation2() example for gwas simulation
+if (!require("devtools")) install.packages("devtools")
+#### Part A: Haemodynamic response functions (HRF) and block design
+## Plot Basic HRF from 0-20s
+hq <- function(t,q=4){
+# q=4 or 5, where 5 has more of a delay
+return (t^q * exp(-t)/(q^q * exp(-q)))
+}
+# use seq to create vector time and use hq to create hrf vectors
+time <- seq(1,20)
+time
+# use seq to create vector time and use hq to create hrf vectors
+time <- seq(0,20)
+hq
+# use seq to create vector time and use hq to create hrf vectors
+time <- seq(0,20)
+hrf1 <- hq(time)
+hrf2 <- hq(time, 5)
+# plot
+plot(time,hrf1,type="l")
+lines(time,hrf2,col="red")
+## Deconvolve with task onset times
+# grabbed from afni c code
+# basis_block_hrf4 from 3dDeconvolve.c
+HRF <- function(t, d){
+if (t<0){
+y=0.0
+}else{
+y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
+}
+return(y)
+}
+t=seq(0,360,len=360)
+onsets=c(14,174,254)
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+plot(blocks.model, type="l")
+lines(time,hrf1,col="red")
+pwd
+ls
+voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
+## Set Working Directory to file directory - RStudio approach
+setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
+voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
+voxel_time
+plot(blocks.model, type="l")
+lines(voxel_time,hrf1,col="red")
+voxel_time <- scan("059_069_025.1D", character(), quote = "\n")
+t=seq(0,max(voxel_time))
+blocks.model = double()
+for (curr_t in voxel_time){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+for (curr_t in t){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in voxel_time){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+voxel_time
+onsets
+class(onsets)
+class(voxel_time)
+voxel_time <- as.numeric(scan("059_069_025.1D", character(), quote = "\n"))
+t=seq(0,max(voxel_time))
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in voxel_time){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+## Plot voxel time series data and the block design curve
+voxel.data <- read.delim("059_069_025.1D")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# normalize the height of the blocks model
+blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
+lines(blocks.normal,type="l",col="red")
+# regression
+length(blocks.normal) # too long
+dim(voxel.data)[1]
+# grab elements from blocks.normal to make a vector same as data
+blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
+length(blocks.norm.subset)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# normalize the height of the blocks model
+blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
+lines(blocks.normal,type="l",col="red")
+# regression
+length(blocks.normal) # too long
+dim(voxel.data)[1]
+# grab elements from blocks.normal to make a vector same as data
+blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
+length(blocks.norm.subset)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+# use lm to create voxel.fit <- lm...
+voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+# use abline(voxel.fit) to overlay a line with fit coefficients
+abline(voxel.fit)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+length(blocks.norm.subset)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+length(voxel.data.vec)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+blocks.norm.subset
+voxel.data.vec
+voxel.fit <- lm(blocks.norm.subet ~ voxel.data.vec)
+voxel.fit <- lm(blocks.norm.subset ~ voxel.data.vec)
+# use abline(voxel.fit) to overlay a line with fit coefficients
+abline(voxel.fit)
+## Plot voxel time series data and the block design curve
+voxel.data <- read.delim("059_069_025.1D")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# use lm to create voxel.fit <- lm...
+voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+# use abline(voxel.fit) to overlay a line with fit coefficients
+abline(voxel.fit)
+voxel.fitr
+voxel.fit
+voxel.data
+blocks.normal
+blocks.model
+max(blocks.model)
+t=seq(0,360,len=360)
+onsets=c(14,174,254)
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+## Plot voxel time series data and the block design curve
+voxel.data <- read.delim("059_069_025.1D")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# normalize the height of the blocks model
+blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
+lines(blocks.normal,type="l",col="red")
+# regression
+length(blocks.normal) # too long
+# Lab 11 for the University of Tulsa's CS-6643 Bioinformatics Course
+# Introduction to fMRI Analysis and ICA
+# Professor: Dr. McKinney, Fall 2022
+# Noah L. Schrick - 1492657
+## Set Working Directory to file directory - RStudio approach
+setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
+#### Part A: Haemodynamic response functions (HRF) and block design
+## Plot Basic HRF from 0-20s
+hq <- function(t,q=4){
+# q=4 or 5, where 5 has more of a delay
+return (t^q * exp(-t)/(q^q * exp(-q)))
+}
+# use seq to create vector time and use hq to create hrf vectors
+time <- seq(0,20)
+hrf1 <- hq(time)
+hrf2 <- hq(time, 5)
+# plot
+plot(time,hrf1,type="l")
+lines(time,hrf2,col="red")
+## Deconvolve with task onset times
+# grabbed from afni c code
+# basis_block_hrf4 from 3dDeconvolve.c
+HRF <- function(t, d){
+if (t<0){
+y=0.0
+}else{
+y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
+}
+return(y)
+}
+t=seq(0,360,len=360)
+onsets=c(14,174,254)
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+## Plot voxel time series data and the block design curve
+voxel.data <- read.delim("059_069_025.1D")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# normalize the height of the blocks model
+blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
+lines(blocks.normal,type="l",col="red")
+# regression
+length(blocks.normal) # too long
+dim(voxel.data)[1]
+# grab elements from blocks.normal to make a vector same as data
+blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
+length(blocks.norm.subset)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+# use lm to create voxel.fit <- lm...
+voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+# use abline(voxel.fit) to overlay a line with fit coefficients
+abline(voxel.fit)
+# Lab 11 for the University of Tulsa's CS-6643 Bioinformatics Course
+# Introduction to fMRI Analysis and ICA
+# Professor: Dr. McKinney, Fall 2022
+# Noah L. Schrick - 1492657
+## Set Working Directory to file directory - RStudio approach
+setwd(dirname(rstudioapi::getActiveDocumentContext()$path))
+#### Part A: Haemodynamic response functions (HRF) and block design
+## Plot Basic HRF from 0-20s
+hq <- function(t,q=4){
+# q=4 or 5, where 5 has more of a delay
+return (t^q * exp(-t)/(q^q * exp(-q)))
+}
+# use seq to create vector time and use hq to create hrf vectors
+time <- seq(0,20)
+hrf1 <- hq(time)
+hrf2 <- hq(time, 5)
+# plot
+plot(time,hrf1,type="l")
+lines(time,hrf2,col="red")
+## Deconvolve with task onset times
+# grabbed from afni c code
+# basis_block_hrf4 from 3dDeconvolve.c
+HRF <- function(t, d){
+if (t<0){
+y=0.0
+}else{
+y = 1/256*exp(4-t)*(-24-24*t-12*t^2-4*t^3-t^4 + exp(min(d,t))*(24+24*(t-min(d,t)) + 12*(t-min(d,t))^2+4*(t-min(d,t))^3+(t-min(d,t))^4))
+}
+return(y)
+}
+t=seq(0,360,len=360)
+onsets=c(14,174,254)
+blocks.model = double()
+for (curr_t in t){
+summed_hrf=0.0
+for (start in onsets){
+summed_hrf=summed_hrf+HRF(curr_t-start,20)
+}
+blocks.model = c(blocks.model,summed_hrf)
+}
+plot(blocks.model,type="l")
+## Plot voxel time series data and the block design curve
+voxel.data <- read.delim("059_069_025.1D")
+plot(seq(1,2*dim(voxel.data)[1],by=2),t(voxel.data),
+type="l", xlab="time",ylab="intensity")
+# normalize the height of the blocks model
+blocks.normal <- max(voxel.data)*blocks.model/max(blocks.model)
+lines(blocks.normal,type="l",col="red")
+# regression
+length(blocks.normal) # too long
+dim(voxel.data)[1]
+# grab elements from blocks.normal to make a vector same as data
+blocks.norm.subset <- blocks.normal[seq(1,length(blocks.normal),len=dim(voxel.data)[1])]
+length(blocks.norm.subset)
+voxel.data.vec <- matrix(unlist(voxel.data),ncol=1)
+# use lm to create voxel.fit <- lm...
+voxel.fit <- lm(voxel.data.vec ~ blocks.norm.subset)
+plot(blocks.norm.subset,voxel.data.vec,
+xlab="block model",ylab="voxel data",main="regression fit")
+# use abline(voxel.fit) to overlay a line with fit coefficients
+abline(voxel.fit)
+blocks.model
+count(blocks.model > 1)
+which(blocks.model > 1)
+sum(blocks.model < 1)
+length(blocks.model)
+100* sum(blocks.model < 1)/length(blocks.model)
+#### Part B: Resting state fMRI visualization, multidimensional arrays and independent component analysis (ICA).
+## example: multi-dimensional array
+#                        2 3x4 matrices
+multArray <- array(1:24,dim=c(3,4,2))
+dim(multArray)
+multArray[,,1] # matrix 1
+multArray[,,2] # matrix 2
+image(multArray[,,1]) # plot slice 1
+image(multArray[,,2]) # plot slice 2
+dim(multArray)
+size(multArray)
+length(multArray)
+multArray
+multArray[,,1] # matrix 1
+multArray[,,2] # matrix 2
+image(multArray[,,1]) # plot slice 1
+image(multArray[,,2]) # plot slice 2
+image(multArray[,,1]) # plot slice 1
+image(multArray[,,2]) # plot slice 2
+## Neuroimaging Informatics Technology Initiative
+if (!require("fastICA")) install.packages("fastICA")
+if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
+if (!require("fmri")) install.packages("fmri")
+#    If this fails, try library(devtools) (install.packages("devtools"))
+#    and then install_github(https://github.com/cran/fmri.git)
+library(fmri)
+## Neuroimaging Informatics Technology Initiative
+if (!require("fastICA")) install.packages("fastICA")
+if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
+install.packages("R.matlab")
+install.packages("Biostrings")
+BiocManager::install("Biostrings")
+BiocManager::install("Biostrings")
+BiocManager::install("AnalyzeFMRI")
+BiocManager::install()
+if (!require("fmri")) install.packages("fmri")
+if (!require("fmri")) install.packages("aws")
+if (!require("fmri")) install.packages("gsl")
+install.packages("gsl")
+install.packages("GSL")
+install_github(https://github.com/cran/fmri.git)
+install_github("https://github.com/cran/fmri.git")
+#    If this fails, try library(devtools) (install.packages("devtools"))
+#    and then install_github(https://github.com/cran/fmri.git)
+if (!require("devtools")) install.packages("devtools")
+library(devtools)
+install_github("https://github.com/cran/fmri.git")
+install_github("https://github.com/cran/aws.git")
+install_github("https://github.com/cran/gsl.git")
+#    If this fails, try library(devtools) (insta
+install.packages("gsl")
+install.packages("fmri")
+if (!require("AnalyzeFMRI")) install.packages("AnalyzeFMRI")
+if (!require("fastICA")) install.packages("fastICA")
+library(fastICA)
+# read in 4d nifti
+# uses fmri library, takes about 3min to load
+img <- read.NIFTI("rest_res2standard.nii")
+library(fmri)
+# read in 4d nifti
+# uses fmri library, takes about 3min to load
+img <- read.NIFTI("rest_res2standard.nii")
+mask <- img$mask  # Boolean mask for brain voxels
+dim(mask)
+ttt <- extractData(img) # extract 4d data cube
+numScans <- dim(ttt)[4]
+# plot a voxel's time series
+plot(ttt[30,30,30,],type="l",xlab="time",ylab="activity")
+length(ttt)
+ttt
+dim(ttt)
+length(ttt)
+numScans
+## Plot a 2D Slice
+yslice <- 35
+scan2dslice <- ttt[,yslice,,50] # grab 2d slice at t=50
+image(scan2dslice,main="no masking") # no mask
+# mask it off
+slice.mask <- mask[,yslice,]
+scan2dslice[slice.mask] <- NA # NA's become white
+image(scan2dslice,main="masked")
+mask
+slice.mask
+## ICA
+t1 <- Sys.time() # for timing purposes
+dataMat <- NULL
+for(t in seq(1,numScans)){
+scan <- ttt[,,,t]
+# stretched out the 61x73x61 3d matrix into one row
+# apply mask and stack
+dataMat <- rbind(dataMat,scan[mask])
+}
+t2 <- Sys.time()
+difftime(t2,t1) # 3 minutes
+dim(dataMat)
+dataMat
+dataMat[1,]
+dataMat[99,]
+## ICA analysis
+# input X: rows observations (voxels) and cols variables (time)
+X <- t(dataMat)
+m <- 20 # specify number of ICA components
+t1<-Sys.time()
+f<-fastICA(X,n.comp=m,method="C")
+t2<-Sys.time()
+difftime(t2,t1) # 1.23min
+# S=XKW,
+# K is a pre-whitening PCA matrix (components by time)
+# S is the matrix of m ICAs (columns of S are spatial signals)
+# S has dimensions voxel x components
+S<-f$S  # you can find K and W with $
+S
+dim(S)
+dim(f$K)
+dim(f$W)
+ica.comp <- 5 # look at 5th component
+# plot the 5th time ICA
+plot(f$K[,ica.comp],type="l",xlab="time",ylab="signal",main="ICA component")
+# threshold S matrix
+theta <- 2
+S[S<=theta] <- NA
+# turn S back into 4d multidimensional array
+xdim<-dim(ttt)[1]
+ydim<-dim(ttt)[2]
+zdim<-dim(ttt)[3]
+ica.4dArray <- array(matrix(S,ncol=1),dim=c(xdim,ydim,zdim,m))
+dim(ica.4dArray) # 61x73x61x10
+yslice <- 35
+# grab 2d slice at y=yslice and ica 5
+ica2dslice <- ica.4dArray[,yslice,,ica.comp]
+image(ica2dslice,main="ica component (spatial locations)")

Schrick-Noah_CS-6643_Lab-11.R

@@ -76,3 +76,86 @@ plot(blocks.norm.subset,voxel.data.vec,
 abline(voxel.fit)
 
 
+#### Part B: Resting state fMRI visualization, multidimensional arrays and independent component analysis (ICA). 
+## example: multi-dimensional array 
+#                        2 3x4 matrices
+multArray <- array(1:24,dim=c(3,4,2))
+dim(multArray)
+multArray[,,1] # matrix 1
+multArray[,,2] # matrix 2
+image(multArray[,,1]) # plot slice 1
+image(multArray[,,2]) # plot slice 2
+
+## Neuroimaging Informatics Technology Initiative
+if (!require("fastICA")) install.packages("fastICA")
+if (!require("fmri")) install.packages("fmri")
+library(fastICA)
+library(fmri)
+
+# read in 4d nifti 
+# uses fmri library, takes about 3min to load 
+img <- read.NIFTI("rest_res2standard.nii") 
+
+mask <- img$mask  # Boolean mask for brain voxels
+dim(mask)
+ttt <- extractData(img) # extract 4d data cube
+numScans <- dim(ttt)[4]
+
+# plot a voxel's time series
+plot(ttt[30,30,30,],type="l",xlab="time",ylab="activity")
+
+## Plot a 2D Slice
+yslice <- 35
+scan2dslice <- ttt[,yslice,,50] # grab 2d slice at t=50
+image(scan2dslice,main="no masking") # no mask
+# mask it off
+slice.mask <- mask[,yslice,]
+scan2dslice[slice.mask] <- NA # NA's become white
+image(scan2dslice,main="masked")
+
+## ICA
+t1 <- Sys.time() # for timing purposes
+dataMat <- NULL
+for(t in seq(1,numScans)){
+  scan <- ttt[,,,t]
+  # stretched out the 61x73x61 3d matrix into one row
+  # apply mask and stack 
+  dataMat <- rbind(dataMat,scan[mask])
+}
+t2 <- Sys.time()
+difftime(t2,t1) # 3 minutes
+dim(dataMat)
+
+## ICA analysis
+# input X: rows observations (voxels) and cols variables (time)
+X <- t(dataMat)
+m <- 20 # specify number of ICA components
+t1<-Sys.time()
+f<-fastICA(X,n.comp=m,method="C")
+t2<-Sys.time()
+difftime(t2,t1) # 1.23min
+# S=XKW,
+# K is a pre-whitening PCA matrix (components by time)
+# S is the matrix of m ICAs (columns of S are spatial signals)
+# S has dimensions voxel x components
+S<-f$S  # you can find K and W with $
+
+ica.comp <- 5 # look at 5th component 
+# plot the 5th time ICA
+plot(f$K[,ica.comp],type="l",xlab="time",ylab="signal",main="ICA component")
+
+# threshold S matrix 
+theta <- 2
+S[S<=theta] <- NA
+
+# turn S back into 4d multidimensional array
+xdim<-dim(ttt)[1]
+ydim<-dim(ttt)[2]
+zdim<-dim(ttt)[3]
+ica.4dArray <- array(matrix(S,ncol=1),dim=c(xdim,ydim,zdim,m))
+dim(ica.4dArray) # 61x73x61x10
+yslice <- 35
+# grab 2d slice at y=yslice and ica 5
+ica2dslice <- ica.4dArray[,yslice,,ica.comp] 
+image(ica2dslice,main="ica component (spatial locations)") 
+