DATA605 - Homework4

With the attached data file, build and visualize eigenimagery that accounts for 80% of the variability. Provide full R code and discussion.

Required libraries

library(doParallel)
library(foreach)
library(jpeg)
library(EBImage)
library(OpenImageR)

Use of Graphics

We have 17 files in the zip so we will process the files by setting the num=17

#############Prepare for Image Processing#######################
num=17
files=list.files("D:/MSProjects/605/week4/jpg/",pattern="\\.jpg")[1:num] 
################################################################

View Shoes Function

###################Set Adj. Parameters##########################
height=1200; width=2500;scale=20
plot_jpeg = function(path, add=FALSE)
{ jpg = readJPEG(path, native=T) # read the file
  res = dim(jpg)[2:1] # get the resolution, [x, y]
  if (!add) # initialize an empty plot area if add==FALSE
    plot(1,1,xlim=c(1,res[1]),ylim=c(1,res[2]),asp=1,type='n',xaxs='i',yaxs='i',xaxt='n',yaxt='n',xlab='',ylab='',bty='n')
  rasterImage(jpg,1,1,res[1],res[2])
}
################################################################

Load the Data into an Array

Loading the data into the array with required dimensions. Resize function scales the images to the specified dimensions.

###################Load#########################
im=array(rep(0,length(files)*height/scale*width/scale*3), dim=c(length(files), height/scale, width/scale,3))

for (i in 1:17){
  temp=resize(readJPEG(paste0("D:/MSProjects/605/week4/jpg/", files[i])),height/scale, width/scale)
  im[i,,,]=array(temp,dim=c(1, height/scale, width/scale,3))}

#################################################

Vectorize

Here we vecorize the array with dimensions as -> number of files * (ht/scl * wt/scl * 3)

#################################################
flat=matrix(0, 17, prod(dim(im))) 
for (i in 1:17) {
  newim <- readJPEG(paste0("D:/MSProjects/605/week4/jpg/", files[i]))
  r=as.vector(im[i,,,1]); g=as.vector(im[i,,,2]);b=as.vector(im[i,,,3])
  flat[i,] <- t(c(r, g, b))
}
shoes=as.data.frame(t(flat))
#################################################

Actual Plots

Visualize the actual plots

####Old Shoes##################
par(mfrow=c(3,3))
par(mai=c(.3,.3,.3,.3))
for (i in 1:17){  #plot the first images only
plot_jpeg(writeJPEG(im[i,,,]))
}

###############################

Eigencomponents from Correlation Structure

#################################################
scaled=scale(shoes, center = TRUE, scale = TRUE)
mean.shoe=attr(scaled, "scaled:center") #saving for classification
std.shoe=attr(scaled, "scaled:scale")  #saving for classification...later
#################################################

Calculate Covariance (Correlation)

#################################################
Sigma_=cor(scaled)
#################################################

Get the Eigencomponents

#################################################
myeigen=eigen(Sigma_)
cumsum(myeigen$values) / sum(myeigen$values)

##  [1] 0.6928202 0.7940449 0.8451072 0.8723847 0.8913841 0.9076337 0.9216282
##  [8] 0.9336889 0.9433871 0.9524454 0.9609037 0.9688907 0.9765235 0.9832209
## [15] 0.9894033 0.9953587 1.0000000

#################################################

Eigenshoes

From the above we see the 80% variability can be found at position 2, accordingly we find the eigenshoes at [, 2]

#################################################
scaling=diag(myeigen$values[1:2]^(-1/2)) / (sqrt(nrow(scaled)-1))
eigenshoes=scaled%*%myeigen$vectors[,1:2]%*%scaling
imageShow(array(eigenshoes[,2], c(60,125,3)))

#################################################