DATA 605 Week 4: Eigenshoes

Eigenshoes

Load Libraries

library(jpeg)
library(imager)
library(knitr)
library(dplyr)
files = list.files(path = '/Users/kristinlussi/Documents/MSDS/DATA 605/Week 4/jpg', pattern="\\.jpg")

View Images

# plot layout
par(mfrow = c(4, 5), mar = c(0.5, 0.5, 0.5, 0.5))

for (file in files) {
  filepath <- file.path("/Users/kristinlussi/Documents/MSDS/DATA 605/Week 4/jpg", file)
  img <- readJPEG(filepath)
  plot(0:1, 0:1, type = "n", xlab = "", ylab = "", xlim = c(0, 1), ylim = c(0, 1), xaxt = "n", yaxt = "n", bty = "n")
  rasterImage(img, 0, 0, 1, 1)
}

Load Images into an Array

# Define image dimensions and scale
height <- 1200
width <- 2500
scale <- 20

# Initialize an array to store resized images
newdata <- array(0, dim = c(length(files), height/scale * width/scale * 3))

# Reshape image data to match expected format for PCA
for (i in 1:length(files)) {
  filepath <- file.path("/Users/kristinlussi/Documents/MSDS/DATA 605/Week 4/jpg", files[i])
  img <- resize(load.image(filepath), height/scale, width/scale)
  newdata[i,] <- as.vector(img)
}

Generate Principal Components

# Perform PCA
mypca <- princomp(t(newdata), scores = TRUE, cor = TRUE)

# Verify that sum of variance is 1
sum(mypca$sdev^2 / sum(mypca$sdev^2))

## [1] 1

# Extract squared eigenvalues
mycomponents <- (mypca$sdev^2) / sum(mypca$sdev^2)

# Sum of squared eigenvalues for the first 4 principal components
sum(mycomponents[1:4]) # the first four components account for 86.5% of the variability

## [1] 0.8652577

# sum of squared eigenvalues for the first 15 principal components 
sum(mycomponents[1:15]) # first 15 components account for 98.8% of the variability

## [1] 0.9878529

Show Eigenshoes

# Transpose the scores matrix
mypca2 <- t(mypca$scores)

# Reshape the scores matrix to match the image dimensions
dim(mypca2) <- c(length(files), height/scale, width/scale, 3)

# plot layout
par(mfrow = c(4, 5), mar = c(0.5, 0.5, 0.5, 0.5))

# Loop over the principal components and plot them
for (i in seq_along(files)) {
  new_img <- as.cimg(mypca2[i,,,])
  plot(0:1, 0:1, type = "n", xlab = "", ylab = "", xlim = c(0, 1), ylim = c(0, 1), xaxt = "n", yaxt = "n", bty = "n")
  rasterImage(new_img, 0, 0, 1, 1)
}