Data605hw4

num=17
files=list.files("C:/RData/Data605/week4/",pattern="\\.jpg")[1:num] 

View Shoes function

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])
}

Loading Data into Array

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("C:/RData/Data605/week4/", files[i])),height/scale, width/scale)
  im[i,,,]=array(temp,dim=c(1, height/scale, width/scale,3))}

Vectorize

flat=matrix(0, 17, prod(dim(im))) 
for (i in 1:17) {
  newim <- readJPEG(paste0("C:/RData/Data605/week4/", 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")
std.shoe=attr(scaled, "scaled:scale") 

## CoVariance
Sigma_=cor(scaled)

## 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

80% variability can be found at position 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)))